arxiv_id stringlengths 9 16 | title stringlengths 0 284 | authors listlengths 1 1.74k | submission_date stringlengths 10 116 | comments stringlengths 0 611 | primary_subject stringclasses 148
values | subjects stringlengths 13 354 | doi stringlengths 26 62 | abstract stringlengths 22 3.93k | file_path stringlengths 23 46 |
|---|---|---|---|---|---|---|---|---|---|
1001.1698 | Competing with oneself: Introducing self-interaction in a model of competitive learning | [
"Gaurang Mahajan",
"Anita Mehta"
] | 11 Jan 2010 (<a href="https://arxiv.org/abs/1001.1698v1">v1</a>), last revised 27 Aug 2010 (this version, v2) | 21 pages, 16 figures; Accepted version, to appear in "Theory in Biosciences" | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Statistical Mechanics (cond-mat.stat-mech) | https://doi.org/10.48550/arXiv.1001.1698 | A competitive learning model was introduced in Ref. 1 (A. Mehta and J. M. Luck, Phys. Rev. E 60, 5, 1999), in which the learning is outcome-related. Every individual chooses between a pair of existing strategies or types, guided by a combination of two factors: tendency to conform to the local majority, \em{and} a pref... | nlin-00.zip/1001.1698.pdf |
2006.10017 | Quasi-stationary states of game-driven systems: a dynamical approach | [
"Sergey Denisov",
"Olga Vershinina",
"Juzar Thingna",
"Peter Hänggi",
"Mikhail Ivanchenko"
] | 17 Jun 2020 (<a href="https://arxiv.org/abs/2006.10017v1">v1</a>), last revised 31 Dec 2020 (this version, v2) | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Statistical Mechanics (cond-mat.stat-mech) | https://doi.org/10.48550/arXiv.2006.10017 | Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two complementary approaches to modeling evolution of player populations. The fi... | nlin-00.zip/2006.10017.pdf | |
0901.4083 | Diverse routes to oscillation death in a coupled oscillator system | [
"J.J.Suarez-Vargas",
"J.A. Gonzalez",
"A. Stefanovska",
"P.V.E. McClintock"
] | 26 Jan 2009 | 6 pages, 6 figures, to be published in Europhysics Letters (Feb 2009) | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Medical Physics (physics.med-ph); Tissues and Organs (q-bio.TO) | https://doi.org/10.48550/arXiv.0901.4083 | We study oscillation death (OD) in a well-known coupled-oscillator system that has been used to model cardiovascular phenomena. We derive exact analytic conditions that allow the prediction of OD through the two known bifurcation routes, in the same model, and for different numbers of coupled oscillators. Our exact ana... | nlin-00.zip/0901.4083.pdf |
2006.03887 | Multiple-timescale Neural Networks: Generation of Context-dependent Sequences and Inference through Autonomous Bifurcations | [
"Tomoki Kurikawa",
"Kunihiko Kaneko"
] | 6 Jun 2020 (<a href="https://arxiv.org/abs/2006.03887v1">v1</a>), last revised 2 Mar 2021 (this version, v2) | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Biological Physics (physics.bio-ph) | https://doi.org/10.48550/arXiv.2006.03887 | Sequential transitions between metastable states are ubiquitously observed in the neural system and underlie various cognitive functions. Although a number of studies with asymmetric Hebbian connectivity have investigated how such sequences are generated, the focused sequences are simple Markov ones. On the other hand,... | nlin-00.zip/2006.03887.pdf | |
2305.04538 | Self-induced-stochastic-resonance breathing chimeras | [
"Jinjie Zhu",
"Marius E. Yamakou"
] | 8 May 2023 | 6 pages, 4 figures, 38 references | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.2305.04538 | The study in [Phys. Rev. Lett. 117, 014102 (2016)] discovered a novel type of chimera state known as coherence-resonance chimera (CRC), which combines the effects of coherence resonance (CR) and the spatial property of classical chimeras. In this Letter, we present yet another novel form of chimera, which we refer to a... | nlin-00.zip/2305.04538.pdf |
2001.03727 | Amplitude chimera and chimera death induced by external dynamical agents | [
"Umesh Kumar Verma",
"G. Ambika"
] | 11 Jan 2020 (<a href="https://arxiv.org/abs/2001.03727v1">v1</a>), last revised 12 Jun 2020 (this version, v2) | 11 pages, 9 figures | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Physics and Society (physics.soc-ph) | https://doi.org/10.48550/arXiv.2001.03727 | We report the emergence of stable amplitude chimeras and chimera death in a two-layer network where one layer has an ensemble of identical nonlinear oscillators interacting directly through local coupling and indirectly through dynamic agents that form the second layer. The nonlocality in the interaction among the dyna... | nlin-00.zip/2001.03727.pdf |
1810.04574 | Using reservoir computers to distinguish chaotic signals | [
"Thomas L. Carroll"
] | 21 Sep 2018 | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.1810.04574 | Several recent papers have shown that reservoir computers are useful for analyzing and predicting dynamical systems. Reservoir computers have also been shown to be useful for various classification problems. In this work, a reservoir computer is used to identify one out of the 19 different Sprott systems. An advantage ... | nlin-00.zip/1810.04574.pdf | |
2107.11831 | Edges of inter-layer synchronization in multilayer networks with time-switching links | [
"Muhittin Cenk Eser",
"Everton S. Medeiros",
"Mustafa Riza",
"Anna Zakharova"
] | 25 Jul 2021 | 7 pages, 7 figures | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.2107.11831 | We investigate the transition to synchronization in a two-layer network with time-switching inter-layer links. We focus on the role of the number of inter-layer links and the time-scale of topological changes. Initially, we observe a smooth transition to complete synchronization for the static inter-layer topology by i... | nlin-00.zip/2107.11831.pdf |
1207.4401 | How to suppress undesired synchronization | [
"V. H. P. Louzada",
"N. A. M. Araújo",
"J. S. Andrade Jr",
"H. J. Herrmann"
] | 17 Jul 2012 (<a href="https://arxiv.org/abs/1207.4401v1">v1</a>), last revised 2 Oct 2012 (this version, v2) | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Statistical Mechanics (cond-mat.stat-mech); Physics and Society (physics.soc-ph); Neurons and Cognition (q-bio.NC) | https://doi.org/10.48550/arXiv.1207.4401 | It is delightful to observe the emergence of synchronization in the blinking of fireflies to attract partners and preys. Other charming examples of synchronization can also be found in a wide range of phenomena such as, e.g., neurons firing, lasers cascades, chemical reactions, and opinion formation. However, in many s... | nlin-00.zip/1207.4401.pdf | |
0811.3202 | Simple estimates on size of epidemics in generalized SIR-model for inhomogeneous populations | [
"E.Sh.Gutshabash",
"M.M.Brook"
] | 19 Nov 2008 | 5 pages | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.0811.3202 | A generalization of Kermack-McKendick model of epidemics to the case of inhomogeneous susceptibility of population is proposed. Some quantitative and qualitative features of epidemic process development in this situation are established. | nlin-00.zip/0811.3202.pdf |
1411.2805 | Dynamics of Cluster Synchronisation in Modular Networks: Implications for Structural and Functional Networks | [
"Jake Stroud",
"Mauricio Barahona",
"Tiago Pereira"
] | 11 Nov 2014 | to appear as a Chapter at Springer | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.1411.2805 | Experimental results often do not assess network structure; rather, the network structure is inferred by the dynamics of the nodes. From the dynamics of the nodes one then constructs a network of functional relations, termed the functional network. A fundamental question in the analysis of complex systems concerns the ... | nlin-00.zip/1411.2805.pdf |
1107.3085 | Applying whole system design in a sportscar factory | [
"Luca Piancastelli",
"Leonardo Frizziero",
"Simone Marcoppido",
"Eugenio Pezzuti"
] | 15 Jul 2011 | The world crisis had accelerated the necessity to make innovation; innovation must be realized into new products; new innovative products can be thought only new deisgn process | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Software Engineering (cs.SE) | https://doi.org/10.48550/arXiv.1107.3085 | Basing on a paper which explores the adoption of a whole system approach to a more sustainable and innovative design, the present paper wants to apply the same approach to a real case, inside of a famous Italian sportscar factory. A case study in this factory was developed and decodified gaining improved understanding ... | nlin-00.zip/1107.3085.pdf |
2212.07362 | Emergence of intelligent collective motion in a group of agents with memory | [
"Danny Raj Masila",
"Rupesh Mahore"
] | 14 Dec 2022 | 10 pages, 5 figures | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.2212.07362 | Intelligent agents collect and process information from their dynamically evolving neighbourhood to efficiently navigate through it. However, agent-level intelligence does not guarantee that at the level of a collective; a common example is the jamming we observe in traffic flows. In this study, we ask: how and when do... | nlin-00.zip/2212.07362.pdf |
1912.04405 | Explosive higher-order Kuramoto dynamics on simplicial complexes | [
"Ana P. Millán",
"Joaquín J. Torres",
"Ginestra Bianconi"
] | 9 Dec 2019 (<a href="https://arxiv.org/abs/1912.04405v1">v1</a>), last revised 18 May 2020 (this version, v3) | (5 pages, 3 figures) + SM (12 pages, 10 figures) | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Social and Information Networks (cs.SI); Biological Physics (physics.bio-ph); Physics and Society (physics.soc-ph) | https://doi.org/10.48550/arXiv.1912.04405 | The higher-order interactions of complex systems, such as the brain are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make the strong assumption that the dynamics resides exclusively on the nodes. Here we ... | nlin-00.zip/1912.04405.pdf |
nlin/0404012 | Tierra's missing neutrality: case solved | [
"Russell K. Standish"
] | 6 Apr 2004 | Accepted for ALife IX; final MS | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Populations and Evolution (q-bio.PE) | https://doi.org/10.48550/arXiv.nlin/0404012 | The concept of neutral evolutionary networks being a significant factor in evolutionary dynamics was first proposed by Huynen {\em et al.} about 7 years ago. In one sense, the principle is easy to state -- because most mutations to an organism are deleterious, one would expect that neutral mutations that don't affe... | nlin-00.zip/nlin_0404012.pdf |
2101.05383 | Self-driven criticality in a stochastic epidemic model | [
"Gil Ariel",
"Yoram Louzoun"
] | 13 Jan 2021 (<a href="https://arxiv.org/abs/2101.05383v1">v1</a>), last revised 7 Jun 2021 (this version, v2) | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Populations and Evolution (q-bio.PE) | https://doi.org/10.48550/arXiv.2101.05383 | We present a generic epidemic model with stochastic parameters, in which the dynamics self-organize to a critical state with suppressed exponential growth. More precisely, the dynamics evolve into a quasi-steady-state, where the effective reproduction rate fluctuates close to the critical value one, as observed for dif... | nlin-00.zip/2101.05383.pdf | |
nlin/0511024 | The co-evolutionary dynamics of directed network of spin market agents | [
"D. Horvath",
"Z. Kuscsik",
"M. Gmitra"
] | 13 Nov 2005 | 10 pages, 4 figures. accepted for publication in Physica A | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.nlin/0511024 | The spin market model [S. Bornholdt, <a href="http://Int.J.Mod.Phys" rel="external noopener nofollow" class="link-external link-http">this http URL</a>. C 12 (2001) 667] is extended into co-evolutionary version, where strategies of interacting and competitive traders are represented by local and global couplings betwee... | nlin-00.zip/nlin_0511024.pdf |
1712.09609 | Life is not on the edge of chaos but in a half-chaos of not fully random systems. Definition and simulations of the half-chaos in complex networks | [
"Andrzej Gecow"
] | 27 Dec 2017 (<a href="https://arxiv.org/abs/1712.09609v1">v1</a>), last revised 12 Jan 2022 (this version, v4) | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Chaotic Dynamics (nlin.CD) | https://doi.org/10.48550/arXiv.1712.09609 | The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a living, technological or social than fully random Kauffman networks. This makes a lar... | nlin-00.zip/1712.09609.pdf | |
adap-org/9502001 | The Fight Against the Second Law of Thermodynamics | [
"Jorge Berger"
] | 5 Feb 1995 (<a href="https://arxiv.org/abs/adap-org/9502001v1">v1</a>), last revised 15 Jan 1997 (this version, v2) | Latex, 44 pages, 7 figs upon request. | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Astrophysics (astro-ph); Condensed Matter (cond-mat) | https://doi.org/10.48550/arXiv.adap-org/9502001 | After presenting possible motives for fighting against the second law of thermodynamics, several attempts to beat this law are analyzed. The second law wins, but an interesting interpretation of it emerges. This interpretation uses the notion of ``encoded order'' and claims that whether a system is or is not in... | small_categories-00.zip/adap-org_9502001.pdf |
1801.04343 | Susceptibility of power grids to input fluctuations | [
"Stefan Wieland",
"Sébastien Aumaitre",
"Hervé Bercegol"
] | 12 Jan 2018 | 6 pages, 1 figure | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Physics and Society (physics.soc-ph) | https://doi.org/10.48550/arXiv.1801.04343 | With the increasing inclusion of regenerative resources in the energy mix, their intermittent character challenges power grid stability. Hence it is essential to determine which input fluctuations power grids are particularly vulnerable to. Focusing on angular stability in transmission grids, we propose a linear-respon... | nlin-00.zip/1801.04343.pdf |
2105.03894 | Collective dynamics of heterogeneously and nonlinearly coupled phase oscillators | [
"Can Xu",
"Xiaohuan Tang",
"Huaping Lü",
"Karin Alfaro-Bittner",
"Stefano Boccaletti",
"Matjaz Perc",
"Shuguang Guan"
] | 9 May 2021 (<a href="https://arxiv.org/abs/2105.03894v1">v1</a>), last revised 28 Oct 2021 (this version, v2) | 13 pages, 2 figures; accepted for publication in Physical Review Research | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Data Analysis, Statistics and Probability (physics.data-an) | https://doi.org/10.48550/arXiv.2105.03894 | Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak intensity in synchronizing laser arrays. Here we advance this subject by studying a... | nlin-00.zip/2105.03894.pdf |
0904.2439 | Experimental synchronization of circuit oscillations induced by common telegraph noise | [
"Ken Nagai",
"Hiroya Nakao"
] | 16 Apr 2009 | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.0904.2439 | Experimental realization and quantitative investigation of common-noise-induced synchronization of limit-cycle oscillations subject to random telegraph signals are performed using an electronic oscillator circuit. Based on our previous formulation [K. Nagai et al., Phys. Rev. E 71, 036217 (2005)], dynamics of the circu... | nlin-00.zip/0904.2439.pdf | |
nlin/0702053 | A new organizational metrics: A quantum approach | [
"W.F. Lawless",
"Joseph Wood",
"Lily Tung"
] | 26 Feb 2007 | 10 pages, submitted to IEEE SMC 2007 | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.nlin/0702053 | A future goal of robot teams and agent-based models (ABMs) is to field organizations and systems based on first principles derived from human counterparts. Forestalling that opportunity, the failure of traditional organizational theory has at the same time opened the way to innovative theories of organizations and chan... | nlin-00.zip/nlin_0702053.pdf |
1706.06860 | Limit cycles that do not comprise steady states of reactors | [
"Marek Berezowski"
] | 5 Jun 2017 | 9 pages, 6 figures, the paper is printed in Applied Mathematics and Computation, vol. 312, pp. 129-133, 2017 | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.1706.06860 | It is possible that self-induced oscillations appear in reactors, and that their range does not reach the steady state, although such state exists. To prove this, a cascade of tank reactors coupled with mass recycle loop was tested numerically. The above-mentioned phenomenon is characterized by the location of the stea... | nlin-00.zip/1706.06860.pdf |
1108.2376 | Heisenberg uncertainty relation and statistical measures in the square well | [
"Ricardo Lopez-Ruiz",
"Jaime Sanudo"
] | 11 Aug 2011 | 7 pages, 4 figures | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Information Theory (cs.IT); Quantum Physics (quant-ph) | https://doi.org/10.48550/arXiv.1108.2376 | A non stationary state in the one-dimensional infinite square well formed by a combination of the ground state and the first excited one is considered. The statistical complexity and the Fisher-Shannon entropy in position and momentum are calculated with time for this system. These measures are compared with the Heisen... | nlin-00.zip/1108.2376.pdf |
2112.07212 | Self-Organization of Diverse Directional Hierarchical Networks in Simple Coupled Maps with Connection Changes | [
"Taito Nakanishi",
"Masashi Fujii",
"Akinori Awazu"
] | 14 Dec 2021 | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.2112.07212 | We comprehensively studied the morphology of the self-organized effective network structures that form in simple coupled maps with interelement synchronization-dependent connection changes. Based on the parameter values, the spontaneous formation of four types of directional hierarchical networks, named pair-driven net... | nlin-00.zip/2112.07212.pdf | |
2405.01802 | Robust undulatory locomotion via neuromechanical adjustments in a dissipative medium | [
"Kenta Ishimoto",
"Clément Moreau",
"Johann Herault"
] | 3 May 2024 | 13 pages, 9 figures | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Biological Physics (physics.bio-ph) | https://doi.org/10.48550/arXiv.2405.01802 | Dissipative environments are ubiquitous in nature, from microscopic swimmers in low-Reynolds-number fluids to macroscopic animals in frictional media. In this study, motivated by various behaviours of {\it Caenorhabditis elegans} during swimming and crawling locomotion, we consider a mathematical model of a slender ela... | nlin-00.zip/2405.01802.pdf |
1701.05670 | Oscillators that sync and swarm | [
"Kevin P. O'Keeffe",
"Hyunsuk Hong",
"Steven H. Strogatz"
] | 20 Jan 2017 (<a href="https://arxiv.org/abs/1701.05670v1">v1</a>), last revised 1 Sep 2017 (this version, v2) | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.1701.05670 | Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. A complementary form of self-organization occurs among swarming ins... | nlin-00.zip/1701.05670.pdf | |
adap-org/9701001 | Quasi-Linear Cellular Automata | [
"Cristopher Moore"
] | 20 Jan 1997 | 41 pages with figures, To appear in Physica D | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Cellular Automata and Lattice Gases (nlin.CG) | https://doi.org/10.48550/arXiv.adap-org/9701001 | Simulating a cellular automaton (CA) for t time-steps into the future requires t^2 serial computation steps or t parallel ones. However, certain CAs based on an Abelian group, such as addition mod 2, are termed ``linear'' because they obey a principle of superposition. This allows them to be predicted efficient... | small_categories-00.zip/adap-org_9701001.pdf |
2312.08419 | Chaos in Coupled Heteroclinic Cycles between Weak Chimeras | [
"Artyom E. Emelin",
"Evgeny A. Grines",
"Tatiana A. Levanova"
] | 13 Dec 2023 | 15 pages, 8 figures | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Chaotic Dynamics (nlin.CD) | https://doi.org/10.48550/arXiv.2312.08419 | Heteroclinic cycles are widely used in neuroscience in order to mathematically describe different mechanisms of functioning of the brain and nervous system. Heteroclinic cycles and interactions between them can be a source of different types of nontrivial dynamics. For instance, as it was shown earlier, chaotic dynamic... | nlin-00.zip/2312.08419.pdf |
adap-org/9405003 | Evolutionary Learning in the 2D Artificial Life System "Avida" | [
"Chris Adami",
"C. Titus Brown"
] | 16 May 1994 | 5 p., postscript with figures (unpack with uufiles), to appear in the Proc. of ``Artificial Life IV'', MIT Press | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Quantitative Biology (q-bio) | https://doi.org/10.48550/arXiv.adap-org/9405003 | We present a new tierra-inspired artificial life system with local interactions and two-dimensional geometry, based on an update mechanism akin to that of 2D cellular automata. We find that the spatial geometry is conducive to the development of diversity and thus improves adaptive capabilities. We also demonstrate the... | small_categories-00.zip/adap-org_9405003.pdf |
2007.08634 | Effective models and predictability of chaotic multiscale systems via machine learning | [
"Francesco Borra",
"Angelo Vulpiani",
"Massimo Cencini"
] | 2 Jul 2020 (<a href="https://arxiv.org/abs/2007.08634v1">v1</a>), last revised 20 Oct 2020 (this version, v2) | 12 pages with 10 figures. Accepted in Physical Review E | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Machine Learning (cs.LG); Chaotic Dynamics (nlin.CD) | https://doi.org/10.48550/arXiv.2007.08634 | We scrutinize the use of machine learning, based on reservoir computing, to build data-driven effective models of multiscale chaotic systems. We show that, for a wide scale separation, machine learning generates effective models akin to those obtained using multiscale asymptotic techniques and, remarkably, remains effe... | nlin-00.zip/2007.08634.pdf |
1905.12994 | Colored noise in oscillators. Phase-amplitude analysis and a method to avoid the Ito-Stratonovich dilemma | [
"Michele Bonnin",
"Fabio Traversa",
"Fabrizio Bonani"
] | 30 May 2019 | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.1905.12994 | We investigate the effect of time-correlated noise on the phase fluctuations of nonlinear oscillators. The analysis is based on a methodology that transforms a system subject to colored noise, modeled as an Ornstein-Uhlenbeck process, into an equivalent system subject to white Gaussian noise. A description in terms of ... | nlin-00.zip/1905.12994.pdf | |
adap-org/9411002 | Mapping Self-Organized Criticality onto Criticality | [
"Didier Sornette",
"Anders Johansen",
"Ivan Dornic"
] | 28 Nov 1994 | 17 pages total | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.adap-org/9411002 | We present a general conceptual framework for self-organized criticality (SOC), based on the recognition that it is nothing but the expression, ''unfolded'' in a suitable parameter space, of an underlying {\em unstable} dynamical critical point. More precisely, SOC is shown to result from the tuning of ... | small_categories-00.zip/adap-org_9411002.pdf |
1012.2889 | The differences between natural and artificial life. Towards a definition of life | [
"Andrzej Gecow"
] | 13 Dec 2010 (<a href="https://arxiv.org/abs/1012.2889v1">v1</a>), last revised 30 Nov 2011 (this version, v2) | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Other Computer Science (cs.OH); Other Quantitative Biology (q-bio.OT) | https://doi.org/10.48550/arXiv.1012.2889 | It is high time to openly and without finalism define the dangerous but needed term 'purposeful information', whose quantity is an Eigen information value. Using the term 'biological information' in its stead forces one into an uncomfortable detour. I propose such a definition based on the generalized n... | nlin-00.zip/1012.2889.pdf | |
1207.3091 | Hidden stochastic, quantum and dynamic information of Markov diffusion process and its evaluation by an entropy integral measure under the impulse controls actions, applied to information observer | [
"Vladimir S. Lerner"
] | 12 Jul 2012 (<a href="https://arxiv.org/abs/1207.3091v1">v1</a>), last revised 14 May 2019 (this version, v4) | 87 pages | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Information Theory (cs.IT) | https://doi.org/10.48550/arXiv.1207.3091 | Hidden information emerges under impulse interactions with Markov diffusion process modeling interactive random environment. Impulse yes no action cuts Markov correlations revealing Bit of hidden information connected correlated states. Information appears phenomenon of interaction cutting correlations carrying entropy... | nlin-00.zip/1207.3091.pdf |
adap-org/9901001 | The Evolutionary Biology of Ourselves: Unit Requirements and Organizational Change in United States History | [
"Carl Lipo",
"Mark Madsen"
] | 4 Jan 1999 | 23 pages, 3 tables, 12 figures | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.adap-org/9901001 | Researchers have proposed that the distinction between so-called "simple" and "complex" societies can be expressed by an increase in the number of levels at which functional organization, interaction, and thus selection, operate. In spite of the obvious links between this suggestion and research into co... | small_categories-00.zip/adap-org_9901001.pdf |
1901.03119 | Exact universal excitation waveform for optimal enhancement of directed ratchet transport | [
"Ricardo Chacón",
"Pedro J. Martínez"
] | 10 Jan 2019 (<a href="https://arxiv.org/abs/1901.03119v1">v1</a>), last revised 8 May 2020 (this version, v2) | Enlarged version, 8 figures | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Applied Physics (physics.app-ph) | https://doi.org/10.48550/arXiv.1901.03119 | The existence and properties of an exact universal excitation waveform for optimal enhancement of directed ratchet transport are deduced from the criticality scenario giving rise to ratchet universality, and confirmed by numerical experiments in the context of a driven overdamped Brownian particle subjected to a vibrat... | nlin-00.zip/1901.03119.pdf |
1611.01164 | Sensitive Dependence of Optimal Network Dynamics on Network Structure | [
"Takashi Nishikawa",
"Jie Sun",
"Adilson E. Motter"
] | 3 Nov 2016 (<a href="https://arxiv.org/abs/1611.01164v1">v1</a>), last revised 6 Dec 2017 (this version, v3) | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Disordered Systems and Neural Networks (cond-mat.dis-nn); Physics and Society (physics.soc-ph) | https://doi.org/10.48550/arXiv.1611.01164 | The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect to a given performance measure. Here we show that such optimization can lead to s... | nlin-00.zip/1611.01164.pdf | |
1305.6429 | Super-star networks: Growing optimal scale-free networks via likelihood | [
"Michael Small",
"Yingying Li",
"Thomas Stemler",
"Kevin Judd"
] | 28 May 2013 (<a href="https://arxiv.org/abs/1305.6429v1">v1</a>), last revised 11 Nov 2014 (this version, v3) | Draft - extended version of invited talks given in 2013 at Shanghai University, Fudan and Aristotle University of Thessaloniki. Lost the battle with PRL, now significantly expanded (23 pages, 8 figures, 2 appendices) | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Social and Information Networks (cs.SI); Physics and Society (physics.soc-ph) | https://doi.org/10.48550/arXiv.1305.6429 | Preferential attachment --- by which new nodes attach to existing nodes with probability proportional to the existing nodes' degree --- has become the standard growth model for scale-free networks, where the asymptotic probability of a node having degree $k$ is proportional to $k^{-\gamma}$. However, the motivation... | nlin-00.zip/1305.6429.pdf |
1205.0195 | Coherent Pattern Prediction in Swarms of Delay-Coupled Agents | [
"Luis Mier-y-Teran-Romero",
"Eric Forgoston",
"Ira B. Schwartz"
] | 1 May 2012 | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.1205.0195 | We consider a general swarm model of self-propelling agents interacting through a pairwise potential in the presence of noise and communication time delay. Previous work [Phys. Rev. E 77, 035203(R) (2008)] has shown that a communication time delay in the swarm induces a pattern bifurcation that depends on the size of t... | nlin-00.zip/1205.0195.pdf | |
1611.04232 | Chimera states in nonlocally coupled phase oscillators with biharmonic interaction | [
"Hongyan Cheng",
"Qionglin Dai",
"Nianping Wu",
"Yuee Feng",
"Haihong Li",
"Junzhong Yang"
] | 14 Nov 2016 | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.1611.04232 | Chimera states, which consist of coexisting domains of coherent and incoherent parts, have been observed in a variety of systems. Most of previous works on chimera states have taken into account specific form of interaction between oscillators, for example sinusoidal coupling or diffusive coupling. Here, we investigate... | nlin-00.zip/1611.04232.pdf | |
1410.7559 | Erosion of synchronization in networks of coupled oscillators | [
"Per Sebastian Skardal",
"Dane Taylor",
"Jie Sun",
"Alex Arenas"
] | 28 Oct 2014 (<a href="https://arxiv.org/abs/1410.7559v1">v1</a>), last revised 23 Jan 2015 (this version, v2) | 5 pages, 4 figures | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD) | https://doi.org/10.48550/arXiv.1410.7559 | We report erosion of synchronization in networks of coupled phase oscillators, a phenomenon where perfect phase synchronization is unattainable in steady-state, even in the limit of infinite coupling. An analysis reveals that the total erosion is separable into the product of terms characterizing coupling frustration a... | nlin-00.zip/1410.7559.pdf |
2103.09304 | Robust universal approach to identify travelling chimeras and synchronized clusters in spiking networks | [
"Olesia Dogonasheva",
"Dmitry Kasatkin",
"Boris Gutkin",
"Denis Zakharov"
] | 16 Mar 2021 | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.2103.09304 | We propose a robust universal approach to identify multiple dynamical states, including stationary and travelling chimera states based on an adaptive coherence measure. Our approach allows automatic disambiguation of synchronized clusters, travelling waves, chimera states, and asynchronous regimes. In addition, our met... | nlin-00.zip/2103.09304.pdf | |
1808.05975 | Node-Level Resilience Loss in Dynamic Complex Networks | [
"Giannis Moutsinas",
"Weisi Guo"
] | 17 Aug 2018 | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.1808.05975 | In an increasingly connected world, the resilience of networked dynamical systems is important in the fields of ecology, economics, critical infrastructures, and organizational behaviour. Whilst we understand small-scale resilience well, our understanding of large-scale networked resilience is limited. Recent research ... | nlin-00.zip/1808.05975.pdf | |
1912.06470 | Stability of anti-bunched buses and local unidirectional Kuramoto oscillators | [
"Lock Yue Chew",
"Vee-Liem Saw",
"Yi En Ian Pang"
] | 10 Dec 2019 | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Signal Processing (eess.SP); Physics and Society (physics.soc-ph) | https://doi.org/10.48550/arXiv.1912.06470 | Inspired by our recent work that relates bus bunching as a phenomenon of synchronisation of phase oscillators, we construct a model of Kuramoto oscillators that follows an analogous interaction mechanism of local unidirectional coupling. In the bus loop system, we can introduce a no-boarding policy as a form of kicking... | nlin-00.zip/1912.06470.pdf | |
nlin/0505041 | Generalized BBV Models for Weighted Complex Networks | [
"Bo Hu",
"Gang Yan",
"Wen-Xu Wang",
"Wen Chen"
] | 17 May 2005 | 9 pages, 11 figures, submitted to PRE | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.nlin/0505041 | We will introduce two evolving models that characterize weighted complex networks. Though the microscopic dynamics are different, these models are found to bear a similar mathematical framework, and hence exhibit some common behaviors, for example, the power-law distributions and evolution of degree, weight and strengt... | nlin-00.zip/nlin_0505041.pdf |
0707.4028 | The Symmetries and Redundancies of Terror: Patterns in the Dark, A study of Terrorist Network Strategy and Structure | [
"Philip V. Fellman",
"Mark Strathern"
] | 27 Jul 2007 | 13 pages, 3 figures. Proceedings of the 2004 annual meeting of the North American Association for Computation in the Social and Organizational Sciences | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO) | https://doi.org/10.48550/arXiv.0707.4028 | Although much political capital has been made regarding the war on terrorism, and while appropriations have gotten underway, there has been a dearth of deep work on counter-terrorism, and despite massive efforts by the federal government, most cities and states do not have a robust response system. In fact, most do not... | nlin-00.zip/0707.4028.pdf |
2007.01214 | Clusterization and phase diagram of the bimodal Kuramoto model with bounded confidence | [
"André Reggio",
"Robin Delabays",
"Philippe Jacquod"
] | 30 Jun 2020 (<a href="https://arxiv.org/abs/2007.01214v1">v1</a>), last revised 27 Sep 2020 (this version, v2) | 10 pages, 4 figures | Adaptation and Self-Organizing Systems (nlin.AO) | Adaptation and Self-Organizing Systems (nlin.AO); Social and Information Networks (cs.SI); Dynamical Systems (math.DS) | https://doi.org/10.48550/arXiv.2007.01214 | Inspired by the Deffuant and Hegselmann-Krause models of opinion dynamics, we extend the Kuramoto model to account for confidence bounds, i.e., vanishing interactions between pairs of oscillators when their phases differ by more than a certain value. We focus on Kuramoto oscillators with peaked, bimodal distribution of... | nlin-00.zip/2007.01214.pdf |
1904.13331 | Notes on Derived Geometric Formulations in Physics | [
"Kadri İlker Berktav"
] | 29 Apr 2019 (<a href="https://arxiv.org/abs/1904.13331v1">v1</a>), last revised 13 Jul 2023 (this version, v2) | V2: 19 pages; various improvements suggested by an anonymous referee; published in Int. J. Geom. Methods Mod. Phys. Vol. 19, No. 10 (2022) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph) | https://doi.org/10.48550/arXiv.1904.13331 | This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects naturally appear in physics and give rise to formal mathematical treatment, and (iii) t... | math-32-part-2.zip/1904.13331.pdf |
1304.0239 | Examples of topological spaces with arbitrary cohomology jump loci | [
"Botong Wang"
] | 31 Mar 2013 (<a href="https://arxiv.org/abs/1304.0239v1">v1</a>), last revised 2 Apr 2013 (this version, v2) | Carlos Simpson has kindly pointed out to us that the main idea of this paper has been considered in his 1997 survey paper, at least for the case when $k=2$. This is added to the introduction | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Algebraic Topology (math.AT) | https://doi.org/10.48550/arXiv.1304.0239 | Given any subvariety of a complex torus defined over $\mathbb{Z}$ and any positive integer $k$, we construct a finite CW complex $X$ such that the $k$-th cohomology jump locus of $X$ is equal to the chosen subvariety, and the $i$-th cohomology jump loci of $X$ are trivial for $i<k$. | math-31-part-2.zip/1304.0239.pdf |
math/0208106 | Construction of p-adic Hurwitz spaces | [
"Patrick Erik Bradley"
] | 14 Aug 2002 (<a href="https://arxiv.org/abs/math/0208106v1">v1</a>), last revised 11 Sep 2002 (this version, v2) | 16 pages (minor corrections) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0208106 | Moduli spaces for Galois covers of p-adic Mumford curves by Mumford curves are constructed using Herrlich's Teichmuller spaces, Andre's orbifold fundamental groups, and Kato's graphs of groups encoding ramification data of charts for Mumford orbifolds. | math-34-part-1.zip/math_0208106.pdf |
2112.03776 | Seshadri stratifications and standard monomial theory | [
"Rocco Chirivì",
"Xin Fang",
"Peter Littelmann"
] | 7 Dec 2021 (<a href="https://arxiv.org/abs/2112.03776v1">v1</a>), last revised 22 Jun 2023 (this version, v2) | 76 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.2112.03776 | We introduce the notion of a Seshadri stratification on an embedded projective variety. Such a structure enables us to construct a Newton-Okounkov simplicial complex and a flat degeneration of the projective variety into a union of toric varieties. We show that the Seshadri stratification provides a geometric setup for... | math-33-part-1.zip/2112.03776.pdf |
2204.05866 | Generators for the cohomology ring of the moduli of one-dimensional sheaves on $\mathbb{P}^2$ | [
"Weite Pi",
"Junliang Shen"
] | 12 Apr 2022 (<a href="https://arxiv.org/abs/2204.05866v1">v1</a>), last revised 21 Sep 2022 (this version, v2) | 19 pages, final version to appear at Algebraic Geometry | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2204.05866 | We explore the structure of the cohomology ring of the moduli space of stable 1-dimensional sheaves on $\mathbb{P}^2$ of any degree. We obtain a minimal set of tautological generators, which implies an optimal generation result for both the cohomology and the Chow ring of the moduli space. Our approach is through a geo... | math-33-part-1.zip/2204.05866.pdf |
2310.20665 | Irreducibility criteria for the preimages of a transverse variety under endomorphisms of products of elliptic curves | [
"Riccardo Pengo",
"Evelina Viada"
] | 31 Oct 2023 (<a href="https://arxiv.org/abs/2310.20665v1">v1</a>), last revised 19 Sep 2024 (this version, v2) | Final version, to appear in the Kyoto Journal of Mathematics | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.2310.20665 | We provide two different proofs of an irreducibility criterion for the preimages of a transverse subvariety of a product of elliptic curves under a diagonal endomorphism of sufficiently large <a href="http://degree.For" rel="external noopener nofollow" class="link-external link-http">this http URL</a> curves, we presen... | math-33-part-2.zip/2310.20665.pdf |
2204.10799 | On some simple geometric structure of affine Deligne-Lusztig varieties for $GL_n$ | [
"Ryosuke Shimada"
] | 22 Apr 2022 | 27 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.2204.10799 | In this paper we study the geometric structure of affine Deligne-Lusztig varieties for $GL_n$ and $b$ basic. We introduce a new condition on $\lambda$. If this is satisfied, then the corresponding affine Deligne-Lusztig variety is the disjoint union of classical Deligne-Lusztig varieties times finite-dimensional affine... | math-33-part-1.zip/2204.10799.pdf |
1511.03133 | A remark on a polynomial mapping $F: \C^n \to \C^{n}$ | [
"Nguyen Thi Bich Thuy"
] | 10 Nov 2015 (<a href="https://arxiv.org/abs/1511.03133v1">v1</a>), last revised 10 Apr 2016 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1511.03133 | In \cite{Valette}, Guillaume and Anna Valette associate singular varieties $V_F$ to a polynomial mapping $F: \C^n \to \C^n$. In the case $F: \C^2 \to \C^2$, if the set $K_0(F)$ of critical values of $F$ is empty, then $F$ is not proper if and only if the 2-dimensional homology or intersection homology (with any pervers... | math-32-part-1.zip/1511.03133.pdf | |
1305.5768 | Identifiable reparametrizations of linear compartment models | [
"Nicolette Meshkat",
"Seth Sullivant"
] | 24 May 2013 (<a href="https://arxiv.org/abs/1305.5768v1">v1</a>), last revised 11 Dec 2013 (this version, v2) | 5 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Dynamical Systems (math.DS) | https://doi.org/10.48550/arXiv.1305.5768 | Identifiability concerns finding which unknown parameters of a model can be quantified from given input-output data. Many linear ODE models, used in systems biology and pharmacokinetics, are unidentifiable, which means that parameters can take on an infinite number of values and yet yield the same input-output data. We... | math-31-part-2.zip/1305.5768.pdf |
0903.3190 | Monads for framed torsion-free sheaves on multi-blow-ups of the projective plane | [
"Abdelmoubine Amar Henni"
] | 18 Mar 2009 (<a href="https://arxiv.org/abs/0903.3190v1">v1</a>), last revised 23 Aug 2011 (this version, v2) | 32 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0903.3190 | We construct monads for framed torsion-free sheaves on blow-ups of the complex projective plane at finitely many distinct points. Using these monads we prove that the moduli space of such sheaves is a smooth algebraic variety. Moreover we construct monads for families of such sheaves parameterized by a noetherian schem... | math-31-part-1.zip/0903.3190.pdf |
1901.07305 | Introduction to derived categories of coherent sheaves | [
"Andreas Hochenegger"
] | 22 Jan 2019 (<a href="https://arxiv.org/abs/1901.07305v1">v1</a>), last revised 28 Aug 2019 (this version, v2) | 24 pages, minor changes, same content as published version | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1901.07305 | In these notes, an introduction to derived categories and derived functors is given. The main focus is the bounded derived category of coherent sheaves on a smooth projective variety. | math-32-part-2.zip/1901.07305.pdf |
2209.08536 | Non-Additive Geometry and Frobenius Correspondences | [
"Shai Haran"
] | 18 Sep 2022 (<a href="https://arxiv.org/abs/2209.08536v1">v1</a>), last revised 26 Feb 2023 (this version, v3) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2209.08536 | The usual language of algebraic geometry is not appropriate for Arithmetical geometry: addition is singular at the real prime. We developed two languages that overcome this problem: one replace rings by the collection of "vectors" or by bi-operads and another based on "matrices" or props. These are the ... | math-33-part-1.zip/2209.08536.pdf | |
1601.04465 | Geometricity for derived categories of algebraic stacks | [
"Daniel Bergh",
"Valery A. Lunts",
"Olaf M. Schnürer"
] | 18 Jan 2016 (<a href="https://arxiv.org/abs/1601.04465v1">v1</a>), last revised 22 Jul 2016 (this version, v2) | 31 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1601.04465 | We prove that the dg category of perfect complexes on a smooth, proper Deligne-Mumford stack over a field of characteristic zero is geometric in the sense of Orlov, and in particular smooth and proper. On the level of triangulated categories, this means that the derived category of perfect complexes embeds as an admiss... | math-32-part-1.zip/1601.04465.pdf |
1806.08513 | Affine differential geometry and affine rotation surfaces: algebraic surfaces invariant under non-Euclidean affine rotations | [
"Juan Gerardo Alcázar",
"Ron Goldman"
] | 22 Jun 2018 (<a href="https://arxiv.org/abs/1806.08513v1">v1</a>), last revised 2 Aug 2019 (this version, v2) | Several corrections with respect to the previous ArXiv version (in particular, two results on parabolic affine rotation surfaces) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1806.08513 | Affine rotation surfaces are a generalization of the well-known surfaces of revolution. Affine rotation surfaces arise naturally within the framework of affine differential geometry, a field started by Blaschke in the first decades of the past century. Affine rotations are the affine equivalents of Euclidean rotations,... | math-32-part-2.zip/1806.08513.pdf |
1603.04808 | Effective cones of cycles on blow-ups of projective space | [
"Izzet Coskun",
"John Lesieutre",
"John Christian Ottem"
] | 15 Mar 2016 | 26 pages; comments welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1603.04808 | In this paper, we study the cones of higher codimension (pseudo)effective cycles on point blow-ups of projective space. We determine bounds on the number of points for which these cones are generated by the classes of linear cycles, and for which these cones are finitely generated. Surprisingly, we discover that for (v... | math-32-part-1.zip/1603.04808.pdf |
2409.11559 | Decorated trees | [
"Pierrette Cassou-Noguès",
"Daniel Daigle"
] | 17 Sep 2024 (<a href="https://arxiv.org/abs/2409.11559v1">v1</a>), last revised 7 Oct 2024 (this version, v2) | We added a definition that was missing (Notation 6.6) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2409.11559 | We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and the decorations are required to satisfy certain conditions. The class o... | math-33-part-2.zip/2409.11559.pdf |
2208.03277 | V-filtrations and minimal exponents for locally complete intersection singularities | [
"Qianyu Chen",
"Bradley Dirks",
"Mircea Mustaţă",
"Sebastián Olano"
] | 5 Aug 2022 (<a href="https://arxiv.org/abs/2208.03277v1">v1</a>), last revised 8 Mar 2024 (this version, v3) | 34 pages; v.2: new, simpler argument for Theorem 1.4. V.3: final version, to appear in Crelle's Journal | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2208.03277 | We define and study a notion of minimal exponent for a locally complete intersection subscheme $Z$ of a smooth complex algebraic variety $X$, extending the invariant defined by Saito in the case of hypersurfaces. Our definition is in terms of the Kashiwara-Malgrange $V$-filtration associated to $Z$. We show that the mi... | math-33-part-1.zip/2208.03277.pdf |
2110.13845 | Concentration Robustness in LP Kinetic Systems | [
"Angelyn R. Lao",
"Patrick Vincent N. Lubenia",
"Daryl M. Magpantay",
"Eduardo R. Mendoza"
] | 26 Oct 2021 | 31 pages, 0 figure | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2110.13845 | For a reaction network with species set $\mathscr{S}$, a log-parametrized (LP) set is a non-empty set of the form $E(P, x^*) = \{x \in \mathbb{R}^\mathscr{S}_> \mid \log x - \log x^* \in P^\perp\}$ where $P$ (called the LP set's flux subspace) is a subspace of $\mathbb{R}^\mathscr{S}$, $x^*$ (called the LP set&#... | math-33-part-1.zip/2110.13845.pdf |
1207.5867 | Bogomolov multipliers and retract rationality for semi-direct products | [
"Ming-chang Kang"
] | 25 Jul 2012 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1207.5867 | Let $G$ be a finite group. The Bogomolov multiplier $B_0(G)$ is constructed as an obstruction to the rationality of $\bm{C}(V)^G$ where $G\to GL(V)$ is a faithful representation over $\bm{C}$. We prove that, for any finite groups $G_1$ and $G_2$, $B_0(G_1\times G_2)\xrightarrow{\sim} B_0(G_1)\times B_0(G_2)$ under the ... | math-31-part-2.zip/1207.5867.pdf | |
0709.3705 | First Steps in Tropical Intersection Theory | [
"Lars Allermann",
"Johannes Rau"
] | 24 Sep 2007 (<a href="https://arxiv.org/abs/0709.3705v1">v1</a>), last revised 20 Jan 2009 (this version, v3) | 37 pages, 10 Postscript figures, version 3 coincides with the version to appear in Mathematische Zeitschrift | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.0709.3705 | We establish first parts of a tropical intersection theory. Namely, we define cycles, Cartier divisors and intersection products between these two (without passing to rational equivalence) and discuss push-forward and pull-back. We do this first for fans in R^n and then for "abstract" cycles that are fans local... | math-30-part-2.zip/0709.3705.pdf |
1411.2640 | Vanishing homology of projective hypersurfaces with 1-dimensional singularities | [
"Dirk Siersma",
"Mihai Tibar"
] | 10 Nov 2014 (<a href="https://arxiv.org/abs/1411.2640v1">v1</a>), last revised 16 May 2017 (this version, v3) | 19 pages, 1 figure, small corrections | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.1411.2640 | We introduce and study the vanishing homology of singular projective hypersurfaces. We prove its concentration in two levels in case of 1-dimensional singular locus $\Sigma$, and moreover determine the ranks of the nontrivial homology groups. These two groups depend on the monodromy at special points of $\Sigma$ and on... | math-31-part-2.zip/1411.2640.pdf |
1311.0940 | Crystalline Hodge cycles and Shimura curves in positive characteristics | [
"Jie Xia"
] | 5 Nov 2013 | 21 pages. Comments welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1311.0940 | In this paper, we seek an appropriate definition for a Shimura curve of Hodge type in positive characteristics, i.e. a characterization of curves in positive characteristics which are reduction of Shimura curve over the complex field. Specifically, we study the liftablity of a curve in moduli space of principally polar... | math-31-part-2.zip/1311.0940.pdf |
2307.01736 | The realization space of a certain conic line arrangement of degree 7 and a $π_1$-equivalent Zariski pair | [
"Meirav Amram",
"Shinzo Bannai",
"Taketo Shirane",
"Uriel Sinichkin",
"Hiro-o Tokunaga"
] | 4 Jul 2023 | 24 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO); Geometric Topology (math.GT) | https://doi.org/10.48550/arXiv.2307.01736 | In this paper, we continue the study of the embedded topology of plane algebraic curves. We study the realization space of conic line arrangements of degree $7$ with certain fixed combinatorics and determine the number of connected components. This is done by showing the existence of a Zariski pair having these combina... | math-33-part-2.zip/2307.01736.pdf |
1412.4381 | Rational connectedness and order of non-degenerate meromorphic maps from\ ${\bf C}^n$ | [
"Frédéric Campana",
"Jörg Winkelmann"
] | 14 Dec 2014 | 9 pages, LaTeX | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.1412.4381 | We show that an $n$-dimensional compact Kähler manifold $X$ admitting a non-degenerate meromorphic map $f:{\bf C}^n\to X$ of order $\rho_f<2$ is rationally connected. | math-31-part-2.zip/1412.4381.pdf |
1507.06891 | Wall divisors and algebraically coisotropic subvarieties of irreducible holomorphic symplectic manifolds | [
"Andreas Leopold Knutsen",
"Margherita Lelli-Chiesa",
"Giovanni Mongardi"
] | 24 Jul 2015 | Comments very welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1507.06891 | Rational curves on Hilbert schemes of points on $K3$ surfaces and generalised Kummer manifolds are constructed by using Brill-Noether theory on nodal curves on the underlying surface. It turns out that all wall divisors can be obtained, up to isometry, as dual divisors to such rational curves. The locus covered by the ... | math-32-part-1.zip/1507.06891.pdf |
1507.08020 | Affine representability results in A^1-homotopy theory II: principal bundles and homogeneous spaces | [
"Aravind Asok",
"Marc Hoyois",
"Matthias Wendt"
] | 29 Jul 2015 (<a href="https://arxiv.org/abs/1507.08020v1">v1</a>), last revised 31 May 2017 (this version, v4) | 45 pages; To appear Geom & Top.; final version before page proofs | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Algebraic Topology (math.AT); Group Theory (math.GR); K-Theory and Homology (math.KT) | https://doi.org/10.48550/arXiv.1507.08020 | We establish a relative version of the abstract "affine representability" theorem in ${\mathbb A}^1$--homotopy theory from Part I of this paper. We then prove some ${\mathbb A}^1$--invariance statements for generically trivial torsors under isotropic reductive groups over infinite fields analogous to the Bass--... | math-32-part-1.zip/1507.08020.pdf |
1008.4299 | Characteristic classes of symmetric products of complex quasi-projective varieties | [
"Sylvain E. Cappell",
"Laurentiu Maxim",
"Joerg Schuermann",
"Julius L. Shaneson",
"Shoji Yokura"
] | 25 Aug 2010 (<a href="https://arxiv.org/abs/1008.4299v1">v1</a>), last revised 24 Jul 2012 (this version, v3) | Paper rewritten to also include generating series formulae for motivic homology Hirzebruch classes, Todd classes of coherent sheaves, as well as Chern classes of constructible sheaves. Some special cases of L-class formulae are also obtained. Moreover, we give a mixed-Hodge-module-free proof for the case of motivic hom... | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1008.4299 | We prove generating series formulae for suitable twisted characteristic classes of symmetric products of a singular complex quasi-projective variety. More concretely, we study homology Hirzebruch classes for motivic coefficients, as well as for complexes of mixed Hodge modules. As a special case, we obtain a generating... | math-31-part-1.zip/1008.4299.pdf |
1710.06692 | Mukai's program (reconstructing a K3 surface from a curve) via wall-crossing | [
"Soheyla Feyzbakhsh"
] | 18 Oct 2017 (<a href="https://arxiv.org/abs/1710.06692v1">v1</a>), last revised 16 Jun 2020 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.1515/crelle-2019-0025 | Let $C$ be a curve of genus $g \geq 11$ such that $g-1$ is a composite number. Suppose $C$ is on a K3 surface whose Picard group is generated by the curve class $[C]$. We use wall-crossing with respect to Bridgeland stability conditions to generalise Mukai's program to this situation: we show how to reconstruct the... | math-32-part-1.zip/1710.06692.pdf | |
alg-geom/9510015 | Rational curves of degree at most 9 on a general quintic threefold | [
"Trygve Johnsen",
"Steven L. Kleiman"
] | 30 Oct 1995 (<a href="https://arxiv.org/abs/alg-geom/9510015v1">v1</a>), last revised 1 Mar 1996 (this version, v2) | 31 pages, minor revisions -- current 2/29/96, Plain Tex | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9510015 | We prove the following form of the Clemens conjecture in low degree. Let $d\le9$, and let $F$ be a general quintic threefold in $\IP^4$. Then (1)~the Hilbert scheme of rational, smooth and irreducible curves of degree $d$ on $F$ is finite, nonempty, and reduced; moreover, each curve is embedded in $F$ with normal bundl... | small_categories-00.zip/alg-geom_9510015.pdf |
1204.4118 | Smith theory and irreducible holomorphic symplectic manifolds | [
"Samuel Boissiere",
"Marc Nieper-Wisskirchen",
"Alessandra Sarti"
] | 18 Apr 2012 (<a href="https://arxiv.org/abs/1204.4118v1">v1</a>), last revised 6 Jul 2012 (this version, v2) | Some results improved. In particular, the main result holds for order three automorphisms | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1204.4118 | We study the cohomological properties of the fixed locus $X^G$ of an automorphism group $G$ of prime order $p$ acting on a variety $X$ whose integral cohomology is torsion-free. We obtain an precise relation between the mod $p$ cohomology of $X^G$ and natural invariants for the action of $G$ on the integral cohomology ... | math-31-part-2.zip/1204.4118.pdf |
math/0112314 | Weight multiplicity free representations, $\frak g$-endomorphism algebras, and Dynkin polynomials | [
"Dmitri I. Panyushev"
] | 31 Dec 2001 (<a href="https://arxiv.org/abs/math/0112314v1">v1</a>), last revised 2 Apr 2002 (this version, v2) | 19 pages, Latex2e; connection with equivariant cohomology is added | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.math/0112314 | $\frak g$-endomorphism algebras form an interesting class of associative algebras related to the adjoint representation of a semisimple Lie algebra $\frak g$. These algebras were recently introduced by <a href="http://A.Kirillov" rel="external noopener nofollow" class="link-external link-http">this http URL</a>, who us... | math-34-part-1.zip/math_0112314.pdf |
1603.06425 | Reduced norms and the Riemann-Roch theorem for Abelian varieties | [
"Nathan Grieve"
] | 21 Mar 2016 (<a href="https://arxiv.org/abs/1603.06425v1">v1</a>), last revised 21 Aug 2017 (this version, v2) | Final Version | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1603.06425 | We explain how the Riemann-Roch theorem for divisors on an abelian variety $A$ is related to the reduced norms of the Wedderburn components of $\operatorname{End}^0(A)$ the $\mathbb{Q}$-endomorphism algebra of $A$. We then describe consequences and examples. | math-32-part-1.zip/1603.06425.pdf |
math/0611590 | The Hesse pencil of plane cubic curves | [
"Michela Artebani",
"Igor Dolgachev"
] | 19 Nov 2006 (<a href="https://arxiv.org/abs/math/0611590v1">v1</a>), last revised 15 May 2008 (this version, v3) | 22 pages, 1 figure; essential revision to section 7, to appear on L'Enseignement Mathématique | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0611590 | This is a survey of the classical geometry of the Hesse configuration of 12 lines in the projective plane related to inflection points of a plane cubic curve. We also study two K3 surfaces with Picard number 20 which arise naturally in connection with the configuration. | math-34-part-2.zip/math_0611590.pdf |
1009.4055 | A short note on vector bundles on curves | [
"Martin Kreidl"
] | 21 Sep 2010 | 5 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1009.4055 | Beauville and Laszlo give an interpretation of the affine Grassmannian for Gl_n over a field k as a moduli space of, loosely speaking, vector bundles over a projective curve together with a trivialization over the complement of a fixed closed point. In order to establish this correspondence, they have to show that desc... | math-31-part-1.zip/1009.4055.pdf |
2412.16295 | The contraction morphism between maps and quasimaps to toric varieties | [
"Alberto Cobos Rabano"
] | 20 Dec 2024 | 35 pages, 2 figures. Comments welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2412.16295 | Given $X$ a smooth projective toric variety, we construct a morphism from a closed substack of the moduli space of stable maps to $X$ to the moduli space of quasimaps to $X$. If $X$ is Fano, we show that this morphism is surjective. The construction relies on the notion of degree of a quasimap at a base-point, which we... | math-33-part-2.zip/2412.16295.pdf |
1011.6564 | On the semiampleness of the positive part of CKM Zariski decompositions | [
"Salvatore Cacciola"
] | 30 Nov 2010 (<a href="https://arxiv.org/abs/1011.6564v1">v1</a>), last revised 17 Jul 2013 (this version, v4) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1011.6564 | We study graded rings associated to big divisors on LC pairs whose difference with the log-canonical divisor is nef. For divisors that are positive enough at the LC centers of the pair, we prove the finite generation of such rings if the pair is DLT or the dimension is low, given that a Zariski decomposition exists. | math-31-part-1.zip/1011.6564.pdf | |
2108.08934 | Stability condition on Calabi-Yau threefold of complete intersection of quadratic and quartic hypersurfaces | [
"Shengxuan Liu"
] | 19 Aug 2021 (<a href="https://arxiv.org/abs/2108.08934v1">v1</a>), last revised 28 Oct 2022 (this version, v3) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2108.08934 | In this paper, we prove a Clifford type inequality for the curve $X_{2,2,2,4}$, which is the intersection of a quartic and three general quadratics in $\mathbb{P}^5$. We thus prove a stronger Bogomolov-Gieseker inequality for characters of stable vector bundles and stable objects on $X_{2,4}$. Applying the scheme propo... | math-33-part-1.zip/2108.08934.pdf | |
math/0010130 | Algorithms for the Toric Hilbert Scheme | [
"Michael Stillman",
"Bernd Sturmfels",
"Rekha R. Thomas"
] | 12 Oct 2000 | This is a chapter for the forthcoming book "Computations in Algebraic Geometry using Macaulay 2" edited by D. Eisenbud, D. Grayson, M. Stillman and B. Sturmfels | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.math/0010130 | The toric Hilbert scheme parametrizes all algebras isomorphic to a given semigroup algebra as a multigraded vectorspace. All components of the scheme are toric varieties, and among them, there is a fairly well understood coherent component. However, it is unknown whether toric Hilbert schemes are always connected. In t... | math-34-part-1.zip/math_0010130.pdf |
1601.00502 | G-marked moduli spaces | [
"Binru Li"
] | 4 Jan 2016 (<a href="https://arxiv.org/abs/1601.00502v1">v1</a>), last revised 20 May 2016 (this version, v2) | 25 pages, minor changes, a new section (section 5) containing new results has been added | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1601.00502 | The aim of this paper is to investigate the closed subschemes of moduli spaces corresponding to projective varieties which admit an effective action by a given finite group $G$. To achieve this, we introduce the moduli functor $\mathsf{M}^G_h$ of $G$-marked Gorenstein canonical models with Hilbert polynomial $h$, and p... | math-32-part-1.zip/1601.00502.pdf |
1811.12097 | Poincare polynomial for the moduli space $\overline{{\mathcal M}_{0,n}}({\mathbb C})$ and the number of points in $\overline{{\mathcal M}_{0,n}}({\mathbb F}_q)$ | [
"N. Amburg",
"E. Kreines",
"G. Shabat"
] | 29 Nov 2018 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1811.12097 | We obtain a combinatorial proof that the number of points of the space $\overline{{\mathcal M}_{0,n}}({\mathbb F}_q)$ satisfies the recurrent formula for Poincare polynomials of the space $\overline{{\mathcal M}_{0,n}}({\mathbb C})$. | math-32-part-2.zip/1811.12097.pdf | |
2311.11381 | Algorithms for Gromov-Witten Invariants of Elliptic Curves | [
"Firoozeh Aga",
"Janko Boehm",
"Alain Hoffmann",
"Hannah Markwig",
"Ali Traore"
] | 19 Nov 2023 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.2311.11381 | We present an enhanced algorithm for exploring mirror symmetry for elliptic curves through the correspondence of algebraic and tropical geometry, focusing on Gromov-Witten invariants of elliptic curves and, in particular, Hurwitz numbers. We present a new highly efficient algorithm for computing generating series for t... | math-33-part-2.zip/2311.11381.pdf | |
1901.06981 | Conformal blocks from vertex algebras and their connections on $\overline{\mathcal{M}}_{g,n}$ | [
"Chiara Damiolini",
"Angela Gibney",
"Nicola Tarasca"
] | 21 Jan 2019 (<a href="https://arxiv.org/abs/1901.06981v1">v1</a>), last revised 20 Sep 2021 (this version, v3) | 36 pages. Final version, to appear in Geometry & Topology | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Quantum Algebra (math.QA) | https://doi.org/10.48550/arXiv.1901.06981 | We show that coinvariants of modules over vertex operator algebras give rise to quasi-coherent sheaves on moduli of stable pointed curves. These generalize Verlinde bundles or vector bundles of conformal blocks defined using affine Lie algebras studied first by Tsuchiya-Kanie, Tsuchiya-Ueno-Yamada, and extend work of a... | math-32-part-2.zip/1901.06981.pdf |
1605.01913 | Torsion orders of complete intersections | [
"Andre Chatzistamatiou",
"Marc Levine"
] | 6 May 2016 (<a href="https://arxiv.org/abs/1605.01913v1">v1</a>), last revised 29 Nov 2016 (this version, v3) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1605.01913 | By a classical result of Roitman, a complete intersection $X$ of sufficiently small degree admits a rational decomposition of the diagonal. This means that some multiple of the diagonal by a positive integer $N$, when viewed as a cycle in the Chow group, has support in $X\times D\cup F\times X$, for some divisor $D$ an... | math-32-part-1.zip/1605.01913.pdf | |
alg-geom/9605009 | A construction of separated quotient space and boundaries of symmetric spaces | [
"Yu.A.Neretin"
] | 21 May 1996 | 5 pages,amstex | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9605009 | We propose a construction of separated quotient space and apply this construction for simple description of Study-Semple-Satake-Furstenberg-De Concini-Procesi-Oshima boundary of symmetric space | small_categories-00.zip/alg-geom_9605009.pdf |
2307.09284 | The Chow ring of the moduli space of degree $2$ quasi-polarized K3 surfaces | [
"Samir Canning",
"Dragos Oprea",
"Rahul Pandharipande"
] | 18 Jul 2023 (<a href="https://arxiv.org/abs/2307.09284v1">v1</a>), last revised 11 Jun 2024 (this version, v3) | v3: 45 pages. Corrected error, Theorem 1 unchanged, but the relations have changed: relations are given explicitly and the Gorenstein kernel is now 1 dimensional | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2307.09284 | We study the Chow ring with rational coefficients of the moduli space $\mathcal F_{2}$ of quasi-polarized $K3$ surfaces of degree $2$. We find generators, relations, and calculate the Chow Betti numbers. The highest nonvanishing Chow group is $\mathsf A^{17}(\mathcal F_2)\cong {\mathbb{Q}}$. We prove that the Chow ring... | math-33-part-2.zip/2307.09284.pdf |
1210.3780 | Unramified two-dimensional Langlands correspondence | [
"D. V. Osipov"
] | 14 Oct 2012 (<a href="https://arxiv.org/abs/1210.3780v1">v1</a>), last revised 7 Jul 2013 (this version, v3) | 30 pages; corrected typos; to appear in Izvestiya: Mathematics | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Category Theory (math.CT); Number Theory (math.NT); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1210.3780 | In this paper we describe the unramified Langlands correspondence for two-dimensional local fields, we construct a categorical analogue of the unramified principal series representations and study its properties. The main tool for this description is the construction of a central extension. For this (and other) central... | math-31-part-2.zip/1210.3780.pdf |
1611.08515 | Higgs bundles over P^1 and quiver representations | [
"Sergey Mozgovoy"
] | 25 Nov 2016 | 9 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1611.08515 | In this note we prove a new explicit formula for the invariants of moduli spaces of twisted Higgs bundles over P^1 and we relate these invariants to the invariants of moduli spaces of representations of some infinite symmetric quiver. The formula can be easily implemented for computations and it is in agreement with th... | math-32-part-1.zip/1611.08515.pdf |
2107.05205 | Connectedness of affine Deligne-Lusztig varieties for unramified groups | [
"Sian Nie"
] | 12 Jul 2021 (<a href="https://arxiv.org/abs/2107.05205v1">v1</a>), last revised 22 Jul 2021 (this version, v2) | 25 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2107.05205 | For unramified reductive groups, we determine the connected components of affine Deligne-Lusztig varieties in the partial affine flag varieties. Based on the work of Hamacher-Kim and Zhou, this result allows us to verify, in the unramified group case, the He-Rapoport axioms, the ``almost product structure" of Newto... | math-33-part-1.zip/2107.05205.pdf |
2509.14606 | Semiample vector bundles and a characterization of étale trivial vector bundles | [
"Indranil Biswas",
"D. S. Nagaraj"
] | 18 Sep 2025 | Final version | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2509.14606 | We prove that a vector bundle $E$ over a smooth complex projective variety $M$ is étale trivial if and only if $E$ is semiample and $c_1(E) \in H^2(M, {\mathbb Q})$ vanishes. Also, a vector bundle $E$ over a smooth complex projective curve is semiample if and only if it is virtually globally generated. | math-34-part-1.zip/2509.14606.pdf |
1209.2075 | Castelnuovo-Mumford regularity and arithmetic Cohen-Macaulayness of complete bipartite subspace arrangements | [
"Zach Teitler",
"Douglas A. Torrance"
] | 10 Sep 2012 (<a href="https://arxiv.org/abs/1209.2075v1">v1</a>), last revised 4 Aug 2014 (this version, v3) | v3: Minor changes, 5pp | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.1209.2075 | We give the Castelnuovo-Mumford regularity of arrangements of (n-2)-planes in P^n whose incidence graph is a sufficiently large complete bipartite graph, and determine when such arrangements are arithmetically Cohen-Macaulay. | math-31-part-2.zip/1209.2075.pdf |
math/0402243 | Orbifoldes à premi\ere classe de Chern nulle | [
"Frederic Campana"
] | 14 Feb 2004 (<a href="https://arxiv.org/abs/math/0402243v1">v1</a>), last revised 18 Mar 2004 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.math/0402243 | An orbifold version of Bogomolov decomposition theorem is established for compact Kähler spaces with quotient singularities and first Chern class <a href="http://zero.The" rel="external noopener nofollow" class="link-external link-http">this http URL</a> proof is a direct adaptation of the classical smooth case, using ... | math-34-part-1.zip/math_0402243.pdf |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.