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alg-geom/9505018
Rational Blowdowns of Smooth 4-Manifolds
In this paper we introduce a surgical procedure, called a rational blowdown, for a smooth 4-manifold X and determine how this procedure affects both the Donaldson and Seiberg-Witten invariants of X.
1995-05-17
2008-02-03
[ "alg-geom", "math.AG" ]
Ronald Fintushel and Ronald Stern
alg-geom/9505017
On projective plane curves whose complements have finite non-abelian fundamental groups
We construct new examples of singular projective plane curves whose complements have finite and non-abelian fundamental groups, by generalizing the classical three cuspidal quartic curve discovered by Zariski.
1995-05-15
2008-02-03
[ "alg-geom", "math.AG" ]
Ichiro Shimada
alg-geom/9505016
Iitaka-Severi's Conjecture for Complex Threefolds
We prove the following generalization of Severi's Theorem: Let $X$ be a fixed complex variety. Then there exist, up to birational equivalence, only finitely many complex varieties $Y$ of general type of dimension at most three which admit a dominant rational map $f$ from $X$ to Y$.
1995-05-12
2014-12-02
[ "alg-geom", "math.AG" ]
Gerd Dethloff
alg-geom/9505015
Stratified Picard--Lefschetz theory
The monodromy action in the homology of level sets of Morse functions on stratified singular analytic varieties is studied. The local variation operators in both the standard and the intersection homology groups defined by the loops around the critical values of such functions are reduced to similar operators in the ho...
1995-05-11
2015-06-30
[ "alg-geom", "dg-ga", "math.AG", "math.DG" ]
Victor Vassiliev
alg-geom/9505010
Algebraic Barth-Lefschetz theorems
Using results of Hironaka-Matsumura and Faltings, we prove a strong version of the well known Fulton-Hansen connectivity theorem for weighted projective spaces. As a consequence we get the following result. If $Y$ is an irreducible subvariety of the $n$-dimensional projective space (over a field of arbitrary characteri...
1995-05-08
2008-02-03
[ "alg-geom", "math.AG" ]
Lucian Badescu
alg-geom/9505014
Seiberg-Witten Invariants and Rationality of Complex Surfaces
The purpose of this paper is: 1) to explain the Seiberg-Witten invariants, 2) to show that - on a K\"ahler surface - the solutions of the monopole equations can be interpreted as algebraic objects, namely effective divisors, 3) to give - as an application - a short selfcontained proof for the fact that rationality of c...
1995-05-08
2008-02-03
[ "alg-geom", "math.AG" ]
Andrei Teleman and Christian Okonek
alg-geom/9505011
Les Invariants de Seiberg-Witten et la Conjecture de Van De Ven
We give a short proof for the fact that rationality of complex surfaces is a property depending only on the differential structure. Our proof uses the new Seiberg-Witten invariants.
1995-05-08
2008-02-03
[ "alg-geom", "math.AG" ]
Ch. Okonek, A. Teleman
alg-geom/9505012
The Coupled Seiberg-Witten Equations, vortices, and Moduli spaces of stable pairs
We introduce coupled Seiberg-Witten equations, and we prove, using a generalized vortex equation, that, for Kaehler surfaces, the moduli space of solutions of these equations can be identified with a moduli space of holomorphic stable pairs. In the rank 1 case, one recovers Witten's result identifying the space of irre...
1995-05-08
2008-02-03
[ "alg-geom", "math.AG" ]
Ch. Okonek, and A. Teleman
alg-geom/9505013
Seiberg-Witten Invariants and the Van De Ven Conjecture
The purpose of this note is to give a short, selfcontained proof of the following result: A complex surface which is diffeomeorphic to a rational surface is rational.
1995-05-08
2008-02-03
[ "alg-geom", "math.AG" ]
Andrei Teleman and Christian Okonek
alg-geom/9505009
Spectral Covers
This is a survey of various results about spectral covers and their relationship to Higgs bundles. To a G-principal Higgs bundle on a variety S corresponds a cameral cover \widetilde{S} of S (a W-Galois cover, where W is the Weyl group of G) together with a sheaf on \widetilde{S} which in simple cases is a line bundle,...
1995-05-07
2008-02-03
[ "alg-geom", "math.AG" ]
Ron Donagi
alg-geom/9505007
A note on Zariski pairs
A couple of complex projective plane curves are said to make a Zariski pair if they have the same degree and the same type of singularities, but their embeddings in the projective plane are topologically different. In this paper, we present a method to construct certain type of Zariski pairs, and make infinite series o...
1995-05-05
2008-02-03
[ "alg-geom", "math.AG" ]
Ichiro Shimada
alg-geom/9505008
Un crit\`ere d'extension d'un foncteur d\'efini sur les sch\'emas lisses
Let $k$ be a field of characteristic zero. By using Hironaka's desingularisation theorem, we prove an extension criterion for a functor defined on nonsingular k-schemes and taking values on a category of complexes. Roughly speaking, the criterion shows that if such a functor satisfies the standard exact sequence of a b...
1995-05-05
2008-02-03
[ "alg-geom", "math.AG" ]
F. Guill\'en and V. Navarro Aznar
alg-geom/9505005
Sequences of stable bundles over a compact complex surface
When identified with sequences of irreducible Hermitian-Einstein connections, sequences of stable holomorphic bundles of fixed topological type and bounded degree on a compact complex surface equipped with a Gauduchon metric are shown to have strongly convergent subsequences after blowing-up and pulling-back sufficient...
1995-05-05
2008-02-03
[ "alg-geom", "math.AG" ]
Nicholas P. Buchdahl
alg-geom/9505006
Blowups and gauge fields
The relationship between stable holomorphic vector bundles on a compact complex surface and the same such objects on a blowup of the surface is investigated, where "stability" is with respect to a Gauduchon metric on the surface and naturally derived such metrics on the blowup. The main results are: descriptions of h...
1995-05-05
2008-02-03
[ "alg-geom", "math.AG" ]
Nicholas P. Buchdahl
alg-geom/9505004
A weighted version of Zariski's hyperplane section theorem and fundamental groups of complements of plane curves
We formulate and prove a weighted version of Zariski's hyperplane section theorem on the topological fundamental groups of the complements of hypersurfaces in a projective space. As an application, we calculate fundamental groups of the complements of certain singular projective plane curves.
1995-05-04
2008-02-03
[ "alg-geom", "math.AG" ]
Ichiro Shimada
alg-geom/9505003
Bogomolov conjecture over function fields for stable curves with only irreducible fibers (Version 2.0)
Let K be a function field and C a non-isotrivial curve of genus g >= 2 over K. In this paper, we will show that if C has a global stable model with only geometrically irreducible fibers, then Bogomolov conjecture over function fields holds.
1995-05-04
2008-02-03
[ "alg-geom", "math.AG" ]
Atsushi Moriwaki
alg-geom/9505002
Quantum cohomology of flag varieties
We describe a construction of Gromov-Witten invariants for flag varieties and use it to give a presentation for the quantum cohomology ring, by extending the ideas used by Bertram in the case of Grassmannians. This provides a proof for the conjecture of Givental and Kim in [GK].
1995-05-03
2008-02-03
[ "alg-geom", "math.AG" ]
Ionu\c{t} Ciocan-Fontanine
alg-geom/9505001
Pieri's rule for flag manifolds and Schubert polynomials
We establish the formula for multiplication by the class of a special Schubert variety in the integral cohomology ring of the flag manifold. This formula also describes the multiplication of a Schubert polynomial by either an elementary symmetric polynomial or a complete homogeneous symmetric polynomial. Thus, we gener...
1995-05-02
2008-02-03
[ "alg-geom", "math.AG", "math.CO" ]
Frank Sottile
alg-geom/9504017
A Non-Linear Deformation of the Hitchin Dynamical System
Mukai's space, parametrizing simple sheaves on a K3 surface S whose numerical invariants are those of a line bundle on a curve C in S, is interpreted as a deformation of Hitchin's system on C. This is used to show that the nilpotent cone in Mukai space is Lagrangian. In rank 2, components of this nilpotent cone are des...
1995-04-30
2008-02-03
[ "alg-geom", "math.AG" ]
Ron Donagi, Lawrence Ein and Robert Lazarsfeld
alg-geom/9504016
Gauge fixing for logarithmic connections over curves and the Riemann-Hilbert-Problem
We explain in detail the correspondence between algebraic connections over CP^{1}, logarithmic at X = { x_{1},...,x_{n} } \subset CP^{1}, and flat bundles over CP^{1}-X with integer weighted filtrations near each x_{j}. Included is a gauge fixing theorem for logarithmic connections. (Thus far, one could work over any R...
1995-04-29
2008-02-03
[ "alg-geom", "math.AG" ]
Christian Gantz and Brian Steer
alg-geom/9504015
Orbifold Riemann Surfaces and the Yang-Mills-Higgs Equations
We extend Hitchin's results on "The self-duality equations on a Riemann surface" (Proc. LMS (3), vol. 55, 1987) to orbifold Riemann surfaces. We prove existence results for orbifold solutions of the Yang-Mills-Higgs equations and construct the moduli space of solutions. These moduli spaces provide interesting examples ...
1995-04-26
2008-02-03
[ "alg-geom", "math.AG" ]
Ben Nasatyr and Brian Steer
alg-geom/9504014
Relative Geometric Invariant Theory and Universal Moduli Spaces
We expose in detail the principle that the relative geometric invariant theory of equivariant morphisms is related to the GIT for linearizations near the boundary of the $G$-effective ample cone. We then apply this principle to construct and reconstruct various universal moduli spaces. In particular, we constructed the...
1995-04-25
2008-02-03
[ "alg-geom", "math.AG" ]
Yi Hu
alg-geom/9504013
Making enumerative predictions by means of mirror symmetry
Given two Calabi--Yau threefolds which are believed to constitute a mirror pair, there are very precise predictions about the enumerative geometry of rational curves on one of the manifolds which can be made by performing calculations on the other. We review the mechanics of making these predictions, including a discus...
1995-04-24
2008-02-03
[ "alg-geom", "hep-th", "math.AG" ]
David R. Morrison
alg-geom/9504012
On irreducible four--manifolds
We show that minimal symplectic 4--manifolds with $b_2^+ >1$ and with residually finite fundamental groups are irreducible. We also give examples of irreducible orientable four--manifolds with indefinite intersection forms which are not almost complex with respect to either orientation.
1995-04-23
2008-02-03
[ "alg-geom", "math.AG" ]
D. Kotschick
alg-geom/9504011
Picard groups of the moduli spaces of vector bundles over algebraic surfaces
We determined the Picard group of the moduli of rank two stable sheaves on an arbitrary algebraic surface up to finite index
1995-04-16
2008-02-03
[ "alg-geom", "math.AG" ]
Jun Li
alg-geom/9504009
The quantum cohomology of homogeneous varieties
We established the associativity of the quantum cohomologies of homogeneous varieties by using degeneration method in algebraic geometry.
1995-04-16
2008-02-03
[ "alg-geom", "math.AG" ]
Jun Li and Gang Tian
alg-geom/9504010
The first two Betti numbers of the moduli spaces of vector bundles on surfaces
We determined the first two Betti numbers of the moduli of rank two stable sheaves on an arbitrary algebraic surface
1995-04-16
2008-02-03
[ "alg-geom", "math.AG" ]
Jun Li
alg-geom/9504008
Integral Subschemes of Codimension Two
In this paper we study the problem of describing the integral subschemes within a fixed even linkage class $\L$ of subschemes in $\Pn$ of codimension two. In the case that $\L$ is not the class of arithmetically Cohen-Macaulay subschemes, we associate to any $X \in \L$ two invariants $\theta_X$ and $\eta_X$. When taken...
1995-04-15
2015-06-30
[ "alg-geom", "math.AC", "math.AG" ]
Scott Nollet
alg-geom/9504007
Some Donaldson invariants of CP^2
We compute the Donaldson numbers $q_{17}(CP^2)=2540$ and $q_{21}(CP^2)=233208$.
1995-04-13
2008-02-03
[ "alg-geom", "math.AG" ]
Geir Ellingsrud, Joseph Le Potier, and Stein A. Stromme
alg-geom/9504006
Siegel automorphic form corrections of some Lorentzian Kac--Moody Lie algebras
We find automorphic form corrections which are generalized Lorentzian Kac--Moody superalgebras without odd real simple roots (see R. Borcherds \cite{Bo1} -- \cite{Bo7}, V. Kac \cite{Ka1} -- \cite{Ka3}, R. Moody \cite{Mo} and \S~6 of this paper) for two elliptic Lorentzian Kac--Moody algebras of the rank $3$ with a latt...
1995-04-10
2008-02-03
[ "alg-geom", "math.AG" ]
Valeri A. Gritsenko and Viacheslav V. Nikulin
alg-geom/9504005
Intersection-theoretical computations on \Mgbar
We determine necessary conditions for ample divisors in arbitrary genus as well as for very ample divisors in genus 2 and 3. We also compute the intersection numbers $\lambda^9$ and $\lambda_{g-1}^3$ in genus 4. The latter number is relevant for counting curves of higher genus on manifolds, cf. the recent work of Bersh...
1995-04-06
2008-02-03
[ "alg-geom", "math.AG" ]
Carel Faber
alg-geom/9504003
Severi Degrees in Cogenus 3
In this short note, a new computation of the degree of the locus of 3-nodal plane curves in the linear system of degree d plane curves is given. The answer is expressed as a tautological class on a blow-up of the Hilbert scheme of 3 points in the plane. The class is evaluated by the Bott residue formula.
1995-04-06
2015-06-30
[ "alg-geom", "math.AG" ]
J. Harris and R. Pandharipande
alg-geom/9504004
Intersections of Q-Divisors on Kontsevich's Moduli Space $\bar{M}_{0,n}(P^r,d)$ and Enumerative Geometry
The theory of Q-Cartier divisors on the space of n-pointed, genus 0, stable maps to projective space is considered. Generators and Picard numbers are computed. A recursive algorithm computing all top intersection products of Q-Divisors is established. As a corollary, an algorithm computing all characteristic numbers of...
1995-04-06
2008-02-03
[ "alg-geom", "math.AG" ]
R. Pandharipande
alg-geom/9504002
On number of hypersurfaces containing projective curves
Generalizing a classical lemma of Castelnuovo, we characterize rational normal curves (resp. linearly normal elliptic curves) as curves $C\subset \PP^n$ such that the number of linearly independent hypersurfaces $Z\supset C$ of given degree~$m$ is maximal (resp. next to maximal).
1995-04-04
2008-02-03
[ "alg-geom", "math.AG" ]
S. L'vovsky
alg-geom/9504001
Hyperbolic Planes
In this paper we consider a special class of arithmetic quotients of bounded symmetric domains which can roughly be described as higher- dimensional analogues of the Hilbert modular varities. The algebraic groups are defined as the unitary groups over two-dimensional right vector spaces over a division algebra with inv...
1995-04-03
2008-02-03
[ "alg-geom", "math.AG" ]
Bruce Hunt
alg-geom/9503025
Local Homology and Cohomology on Schemes
We prove a sheaf-theoretic derived-category generalization of Greenlees-May duality (a far-reaching generalization of Grothendieck's local duality theorem): for a quasi-compact separated scheme X and a "proregular" subscheme Z---for example, any separated noetherian scheme and any closed subscheme---there is a sort of ...
1995-03-30
2008-02-03
[ "alg-geom", "math.AC", "math.AG" ]
Leovigildo Alonso, Ana Jerem\'ias, and Joseph Lipman
alg-geom/9503024
Degrees of generators of ideals defining subschemes of projective space
For an arithmetically Cohen--Macaulay subscheme of projective space, there is a well-known bound for the highest degree of a minimal generator for the defining ideal of the subscheme, in terms of the Hilbert function. We prove a natural extension of this bound for arbitrary locally Cohen--Macaulay subschemes. We then s...
1995-03-29
2008-02-03
[ "alg-geom", "math.AG" ]
Heath M. Martin and Juan C. Migliore
alg-geom/9503022
Roitman's theorem for singular complex projective surfaces
Let $X$ be a complex projective surface with arbitrary singularities. We construct a generalized Abel--Jacobi map $A_0(X)\to J^2(X)$ and show that it is an isomorphism on torsion subgroups. Here $A_0(X)$ is the appropriate Chow group of smooth 0-cycles of degree 0 on $X$, and $J^2(X)$ is the intermediate Jacobian assoc...
1995-03-29
2008-02-03
[ "alg-geom", "math.AG" ]
L. Barbieri-Viale, C. Pedrini and C. Weibel
alg-geom/9503023
The Mumford relations and the moduli of rank three stable bundles
We find a complete set of relations for the rational cohomology ring of the moduli space of rank three stable bundles over a Riemann surface of genus g and also show that the Pontryagin ring vanishes in degree 12g-8 and greater. The results are obtained by introducing some 'dual' Mumford relations and generalising Kirw...
1995-03-29
2008-02-03
[ "alg-geom", "math.AG" ]
Richard Earl
alg-geom/9503020
Th\'eor\`emes De Connexit\'e Pour Les Produits D'Espaces Projectifs et Les Grassmanniennes
Let $G$ be the Grassmannian $G(d,n)$, let $X$ and $Y$ be complete irreducible varieties, and let $X\rightarrow G$ and $Y\rightarrow G$ be morphisms. Hansen proved that $X \times_G Y$ is connected when $codim f(X) + codim g(Y) < n$. We show that the conclusion holds under the often weaker hypothesis $f(X).g(Y).T\ne 0$, ...
1995-03-28
2015-06-30
[ "alg-geom", "math.AG" ]
Olivier Debarre
alg-geom/9503021
Moduli of pre-$\cal D$-modules, perverse sheaves and the Riemann-Hilbert morphism -I
We construct a moduli scheme for semistable pre-$\D$-modules with prescribed singularities and numerical data on a smooth projective variety. These pre-$\D$-modules are to be viewed as regular holonomic $\D$-modules with `level structure'. We also construct a moduli scheme for perverse sheaves on the variety with presc...
1995-03-28
2008-02-03
[ "alg-geom", "math.AG" ]
Nitin Nitsure and Claude Sabbah
alg-geom/9503018
A gem of the modular universe
We introduce one of the most beautiful algebraic varieties known, a quintic hypersurface in projective five-space, which is invariant under the action of the Weyl group of $E_6$. This variety is intricately related with many other moduli problems, some of which are: marked hyperelliptic curves of genus two, Picard curv...
1995-03-27
2008-02-03
[ "alg-geom", "math.AG" ]
Bruce Hunt
alg-geom/9503019
An orbifold partition of ${\overline{M}_g^n}$
We define a partition of ${\overline{M}_g^n}$ and show that the cohomology of ${\overline{M}_g^n}$ in a given degree admits a filtration whose respective quotients are isomorphic to the shifted cohomology groups of the parts if $g$ is sufficiently large. This implies that the map $H^k({\overline{M}_g^n}) \ra H^k(M_g^n)...
1995-03-27
2008-02-03
[ "alg-geom", "math.AG" ]
Martin Pikaart
alg-geom/9503017
Akizuki's counterexample
Following Akizuki, I construct a Noetherian local integral domain C_M whose normalisation (integral closure) is not finite over C_M. My proof follows closely Akizuki's ingenious calculations.
1995-03-26
2008-02-03
[ "alg-geom", "math.AG" ]
Miles Reid
alg-geom/9503016
On a conjecture of Varchenko
In this note we generalize and prove a recent conjecture of Varchenko concerning the number of critical points of a (multivalued) meromorphic function $\phi$ on an algebraic manifold. Under certain conditions, this number turns out to coincide with the Euler characteristic (up to a sign) of the complement of the diviso...
1995-03-26
2009-10-28
[ "alg-geom", "math.AG" ]
Roberto Silvotti
alg-geom/9503015
The nil Hecke ring and singularity of Schubert varieties
We give a criterion for smoothness of a point in any Schubert variety in any G/B in terms of the nil Hecke ring.
1995-03-24
2015-06-24
[ "alg-geom", "math.AG" ]
Shrawan Kumar
alg-geom/9503013
Moduli spaces of semiquasihomogeneous singularities with fixed principal part
We construct coarse moduli spaces of semiquasihomogeneous hypersurface singularities with respect to right equivalence and contact equivalence. We have to fix the principal part of the semiquasihomogeneous singularities. For the moduli spaces with respect to contact equivalence we also fix the Hilbert function of the T...
1995-03-22
2008-02-03
[ "alg-geom", "math.AG" ]
G.-M. Greuel, C. Hertling, and G. Pfister
alg-geom/9503014
Stable Parabolic Bundles over Elliptic Surfaces and over Orbifold Riemann Surfaces
For an elliptic surface $q:Y \to \Sigma$, with prescribed singular fibres, Stefan Bauer proved directly via algebraic geometry that the stable bundles over $Y$, whose chern classes are pull backs from $\Sigma$, correspond to the stable (V-)bundles over $\Sigma$. We show, via a short proof in differential geometry, a ...
1995-03-22
2008-02-03
[ "alg-geom", "math.AG" ]
Christian Gantz and Brian Steer
alg-geom/9503012
The irreducibility of the moduli space of stable vector bundles of rank 2 on a quintic in $\pp^3$
In this paper I consider a quintic surface in $\pp^3$, general in the sense of Noether-Lefschetz theory. The vector bundles of rank 2 on this surface which are $\mu$-stable with respect to the hyperplane section and have $c_1 = K$, the canonical class of the surface and fixed $c_2$, are parametrized by a moduli space. ...
1995-03-22
2008-02-03
[ "alg-geom", "math.AG" ]
Pieter Nijsse
alg-geom/9503011
Equianalytic and equisingular families of curves on surfaces
We consider flat families of reduced curves on a smooth surface S such that each member C has the same number of singularities of fixed singularity types and the corresponding (locally closed) subscheme H of the Hilbert scheme of S. We are mainly concerned with analytic resp. topological singularity types and give a su...
1995-03-21
2008-02-03
[ "alg-geom", "math.AG" ]
Gert-Martin Greuel, Christoph Lossen
alg-geom/9503010
Hitchin systems, higher Gaudin operators and $r$-matrices
We adapt Hitchin's integrable systems to the case of a punctured curve. In the case of $\CC P^{1}$ and $SL_{n}$-bundles, they are equivalent to systems studied by Garnier. The corresponding quantum systems were identified by B. Feigin, E. Frenkel and N. Reshetikhin with Gaudin systems. We give a formula for the higher ...
1995-03-20
2015-06-30
[ "alg-geom", "hep-th", "math.AG", "nlin.SI", "solv-int" ]
B. Enriquez and V. Rubtsov
alg-geom/9503009
Geometric Properties of the Double-Point Divisor
Let $X^n \subset P^N$ be a nonsingular, nondegenerate projective variety of dimension $n$ and codimension $N-n \ge 2$. Let $|C_X|$ be the linear system determined by the double-point divisor obtained by generically projecting $X$ to a hypersurface in $P^{n+1}$. We classify those varieties for which $C_X$ is not ample, ...
1995-03-17
2008-02-03
[ "alg-geom", "math.AG" ]
Bo Ilic
alg-geom/9503008
Bloch's conjecture revisited
Let $X$ be a non-singular projective complex surface. We can show that Bloch's conjecture (i.e., that if $p_g=0$ then the Albanese kernel vanishes) is equivalent to the following statement: If $p_g(X)=0$ then for any given Zariski open $U\subset X$ and $\omega\in H^2(U,{\bf C})$ there is a smaller Zariski open $V\subse...
1995-03-16
2008-02-03
[ "alg-geom", "math.AG" ]
L. Barbieri-Viale and V. Srinivas
alg-geom/9503007
Quotient Spaces Modulo Algebraic Groups
The paper proves that if a reductive group scheme acts properly on a scheme then the geometric quotient exists as an algebraic space. As a consequence we obtain the existence of the moduli spcace of canonically polarized varieties over Spec Z.
1995-03-16
2008-02-03
[ "alg-geom", "math.AG" ]
J\'anos Koll\'ar
alg-geom/9503006
The Langlands lemma and the Betti numbers of stacks of $G$--bundles on a curve
In this note we show that the Langlands lemma from the theory of Eisenstein series can be used to invert the recursion relation for the Poincar\'e series of the open substack of semi-stable $G$-bundles which was established by Atiyah/Bott and Harder/Narasimhan.
1995-03-14
2008-02-03
[ "alg-geom", "math.AG" ]
G. Laumon, and M. Rapoport
alg-geom/9503005
An algebraic version of Demailly's asymptotic Morse Inequalities
We give an elementary algebraic proof of some asymptotic estimates (called by Demailly asymptotic Morse inequalities) for the dimensions of cohomology groups of the difference of two ample line bundles on a smooth complex projective variety of any dimension.
1995-03-14
2008-02-03
[ "alg-geom", "math.AG" ]
Flavio Angelini
alg-geom/9503004
The canonical class and the $C^\infty$ properties of K\"ahler surfaces
We give a self contained proof using Seiberg Witten invariants that for K\"ahler surfaces with non negative Kodaira dimension (including those with $p_g = 0$) the canonical class of the minimal model and the $(-1)$-curves, are oriented diffeomorphism invariants up to sign. This implies that the Kodaira dimension is det...
1995-03-10
2008-02-03
[ "alg-geom", "dg-ga", "math.AG", "math.DG" ]
Rogier Brussee
alg-geom/9503003
Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac--Moody Lie algebras
This is a continuation of our "Lecture on Kac--Moody Lie algebras of the arithmetic type" \cite{25}. We consider hyperbolic (i.e. signature $(n,1)$) integral symmetric bilinear form $S:M\times M \to {\Bbb Z}$ (i.e. hyperbolic lattice), reflection group $W\subset W(S)$, fundamental polyhedron $\Cal M$ of $W$ and an ac...
1995-03-10
2015-06-24
[ "alg-geom", "hep-th", "math.AG", "math.QA", "q-alg" ]
Viacheslav V. Nikulin
alg-geom/9503002
Homology of iterated semidirect products of free groups
Let $G$ be a group which admits the structure of an iterated semidirect product of finitely generated free groups. We construct a finite, free resolution of the integers over the group ring of $G$. This resolution is used to define representations of groups which act compatibly on $G$, generalizing classical constructi...
1995-03-07
2007-07-02
[ "alg-geom", "math.AG" ]
Daniel C. Cohen and Alexander I. Suciu
alg-geom/9503001
Quasi-parabolic Siegel Formula
The result of Siegel that the Tamagawa number of $SL_r$ over a function field is 1 has an expression purely in terms of vector bundles on a curve, which is known as the Siegel formula. We prove an analogous formula for vector bundles with quasi-parabolic structures. This formula can be used to calculate the Betti numbe...
1995-03-02
2008-02-03
[ "alg-geom", "math.AG" ]
Nitin Nitsure
alg-geom/9502027
On the blowups of numerical Godeaux surfaces
We give a short proof of the following result: Let $X$ be a complex surface of general type. If the canonical divisor of the minimal model of $X$ has selfintersection $= 1$, then $X$ is not diffeomorphic to a rational surface. Our proof is the natural extension of the argument given in our paper in Inventiones Mathemat...
1995-03-01
2010-06-03
[ "alg-geom", "math.AG" ]
D. Kotschick
alg-geom/9502028
Non--trivial harmonic spinors on generic algebraic surfaces
We disprove Hitchin's conjecture to the effect that for a generic complex structure on a simply connected spin complex surface the square root of the canonical bundle has no more cohomology then is predicted by the Riemann--Roch theorem. (This paper will appear in Proc. Amer. Math. Soc.)
1995-03-01
2010-06-03
[ "alg-geom", "math.AG" ]
D. Kotschick
alg-geom/9502026
Algebraic surfaces and Seiberg-Witten invariants
In this revised version, we add some expository material and references and make some minor corrections.
1995-02-27
2008-02-03
[ "alg-geom", "math.AG" ]
Robert Friedman and John W. Morgan
alg-geom/9502025
Linear bound for abelian automorphisms of varieties of general type
We prove: Let $G$ be a finite abelian group acting faithfully on a complex smooth project variety $X$ of general type with numerically effective canonical divisor, of dimension $n$. Then $$|G| \le C(n)K_X^n ,$$ where $C(n)$ depends only on $n$.
1995-02-27
2008-02-03
[ "alg-geom", "math.AG" ]
Gang Xiao
alg-geom/9502024
Traces and Differential Operators over Beilinson Completion Algebras
A Beilinson completion algebra (BCA) A is a complete semilocal algebra over a perfect field k, whose residue fields are high dimensional local fields. In addition A is a semi-topological algebra. The completion of the structure sheaf of an algebraic k-variety along a saturated chain of points is the prototypical exampl...
1995-02-26
2015-06-30
[ "alg-geom", "math.AG" ]
Amnon Yekutieli
alg-geom/9502023
Extremal contractions from 4-dimensional manifolds to 3-folds
Let $g : X \to Y$ be the contraction of an extremal ray of a smooth projective 4-fold $X$ such that $\dim Y=3$. Then $g$ may have a finite number of 2-dimensional fibers. We shall classify those fibers. Especially we shall prove that any two points of such a fiber is joined by a chain of rational curves of length at mo...
1995-02-25
2008-02-03
[ "alg-geom", "math.AG" ]
Yasuyuki Kachi
alg-geom/9502022
Torsion-Free Sheaves and Moduli of Generalized Spin Curves
This article treats compactifications of the space of generalized spin curves. Generalized spin curves, or $r$-spin curves, are pairs $(X,L)$ with $X$ a smooth curve and $L$ a line bundle whose r-th tensor power is isomorphic to the canonical bundle of $X.$ These are a natural generalization of $2$-spin curves (algebra...
1995-02-21
2008-02-03
[ "alg-geom", "math.AG" ]
Tyler J. Jarvis
alg-geom/9502021
Koszul Property and Frobenius Splitting of Schubert Varieties
We show how the Frobenius splitting method of Mehta-Ramanathan implies the Koszul property of projective coordinate rings of Schubert varieties.
1995-02-20
2008-02-03
[ "alg-geom", "math.AG" ]
Roman Bezrukavnikov
alg-geom/9502019
Algebraic cohomology of the moduli space of rank 2 vector bundles on a curve
Let $\MC$ be the moduli space of stable holomorphic vector bundles of rank 2 and fixed determinant of odd degree, over a smooth projective curve $C$. This paper identifies the algebraic cohomology ring $\HA^*(\MC)$, i.e. the subring of the rational cohomology ring $H^*(\MC;\QQ)$ spanned by the fundamental classes of al...
1995-02-17
2008-02-03
[ "alg-geom", "math.AG" ]
V. Balaji, A.D. King and P.E. Newstead
alg-geom/9502020
A Compactification Over $\overline{M}_g$ Of The Universal Moduli Space of Slope-Semistable Vector Bundles
A projective moduli space of pairs (C,E) where E is a slope- semistable torsion free sheaf of uniform rank on a Deligne- Mumford stable curve C is constructed via G.I.T. There is a natural SL x SL action on the relative Quot scheme over the universal curve of the Hilbert scheme of pluricanonical, genus g curves. The G....
1995-02-17
2008-02-03
[ "alg-geom", "math.AG" ]
R. Pandharipande
alg-geom/9502015
Fundamental groups of complements of curves as solvable groups
We discuss the applications of fundamental groups (of complements of curves) computations (and possibly the computations of the second homotopy group as a model over it) to the classification of algebraic surface. We prove that the fundamental group of the complement of the branch curve of a generic projection of a Ver...
1995-02-16
2008-02-03
[ "alg-geom", "math.AG" ]
Boris Moishezon and Mina Teicher
alg-geom/9502016
Embeddings of homogeneous spaces in prime characteristics
Let $G$ be a reductive linear algebraic group. The simplest example of a projective homogeneous $G$-variety in characteristic $p$, not isomorphic to a flag variety, is the divisor $x_0 y_0^p+x_1 y_1^p+x_2 y_2^p=0$ in $P^2\times P^2$, which is $SL_3$ modulo a non-reduced stabilizer containing the upper triangular matric...
1995-02-16
2008-02-03
[ "alg-geom", "math.AG" ]
Niels Lauritzen
alg-geom/9502017
Poncelet theorems
If there is one polygon inscribed into some smooth conic and circumscribed about another one, then there are infinitely many such polygons. This is Poncelet's theorem. The aim of this note is to collect some (mostly classical) versions of this theorem, namely: - Weyr's Poncelet theorem in $P_3$ (1870), - Emch's the...
1995-02-16
2025-04-09
[ "alg-geom", "math.AG" ]
W. Barth, Th. Bauer
alg-geom/9502018
On the cohomology ring of the moduli space of rank 2 vector bundles on a curve
Let $\MS_g$ be the moduli space of stable holomorphic vector bundles of rank 2 and fixed determinant of odd degree over a smooth complex projective curve of genus $g$. This paper proves various properties of the rational cohomology ring $H^*(\MS_g)$. It is shown that the first relation in genus $g$ between the standard...
1995-02-16
2008-02-03
[ "alg-geom", "math.AG" ]
A.D. King, P.E. Newstead
alg-geom/9502014
Self-intersection of dualizing sheaves of arithmetic surfaces with reducible fibers
Let K be an algebraic number field and O_K the ring of integers of K. Let f : X --> Spec(O_K) be a stable arithmetic surface over O_K of genus g >= 2. In this short note, we will prove that if f has a reducible geometric fiber, then the self intersection of dualizing sheaf of X with Arakelov metric is greater than or e...
1995-02-16
2008-02-03
[ "alg-geom", "math.AG" ]
Atsushi Moriwaki
alg-geom/9502013
Abelian automorphism groups of threefolds of general type
This thesis is devoted to the study of abelian automorphism groups of surfaces and $3$-folds of general type over complex number field $\Bbb C$. We obtain a linear bound in $K^3$ for abelian automorphism groups of $3$-folds of general type whose canonical divisor $K$ is numerically effective, and we improve on Xiao's r...
1995-02-15
2008-02-03
[ "alg-geom", "math.AG" ]
Jin-Xing Cai
alg-geom/9502012
k-very ample line bundles on Del Pezzo Surfaces
A $k$-very ample line bundle L on a Del Pezzo Surface is numerically characterized. We find that the set of the exceptional curves and effective divisors with selfintersection zero, $\cal S$, plays a very important rule in checking the nefness and $k$-very ampleness of a line bundle on a Del pezzo Surface. We show that...
1995-02-15
2008-02-03
[ "alg-geom", "math.AG" ]
Sandra Di Rocco
alg-geom/9502009
Braid Group techniques in Complex Geometry V: The fundamental group of the complement of a Veronese generic projection
Computation of the fundamental group of the complement in the complex plane of the branch curve S , of a generic projection of the Veronese surface to the plane is presented. This paper is a continuation of our previous papers: Braid Group Technique I - IV. In I and II we developed algorithms to compute braid monodromy...
1995-02-14
2008-02-03
[ "alg-geom", "math.AG" ]
Mina Teicher and Boris Moishezon
alg-geom/9502011
Height inequality of algebraic points on curves over functional fields
The purpose of this paper is to give a linear and effective height inequality for algebraic points on curves over functional fields. Our height inequality can be viewed as the logarithmic canonical class inequality of a punctured curve over a functional field (a fibered surface minus a section).
1995-02-14
2008-02-03
[ "alg-geom", "math.AG" ]
Sheng-Li Tan
alg-geom/9502010
Operads, Grothendieck topologies and Deformation theory
The idea of the work is to find an invariant way to pass from deformation theory to cohomology, which does not use any explicit cocycles. The appropriate cohomology theory is based on considering sheaves on a certain site. An advantage of the approach is that it enables one to give a simultanious treatement to all type...
1995-02-14
2008-02-03
[ "alg-geom", "math.AG" ]
D.Gaitsgory
alg-geom/9502008
On singularities of ${\cal M}_{I\!\! P^3}(c_1,c_2)$
Let ${\cal M}_{I\!\! P^3}(c_1,c_2)$ be the moduli space of stable rank-$2$ vector bundles on $I\!\! P^3$ with Chern classes $c_1$, $ c_2$. We prove the following results. 1) Let $0 \le \beta < \gamma $ be two integers, ($\gamma \ge 2)$, such that $2\gamma-3\beta>0$; then ${\cal M}_{I\!\! P^3}(0,2\gamma^2-3\beta^2)$ i...
1995-02-13
2015-06-30
[ "alg-geom", "math.AG" ]
Vincenzo Ancona and Giorgio Ottaviani
alg-geom/9502007
Log Sarkisov Program
The purpose of this paper is two-fold. The first is to give a tutorial introduction to the Sarkisov program, a 3-dimensional generalization of Castelnuovo-N\"other Theorem ``untwisting" birational maps between Mori fiber spaces, which was recently established by Corti after Sarkisov and Reid. The second is an attempt...
1995-02-10
2015-06-30
[ "alg-geom", "math.AG" ]
Andrea Bruno and Kenji Matsuki
alg-geom/9502006
Homology of moduli spaces of curves and commutative homotopy algebras
We propose an explicit relation between the cohomology of compactified and noncompactified moduli spaces of algebraic curves with punctures. This relationship generalizes one between commutative algebras and Lie algebras proposed by Lazard, Kontsevich and Ginzburg and Kapranov. More explicitly, we show that the cohomol...
1995-02-08
2008-02-03
[ "alg-geom", "hep-th", "math.AG", "math.QA", "q-alg" ]
Takashi Kimura, Jim Stasheff, and Alexander A. Voronov
alg-geom/9502005
Mirror symmetry for lattice polarized K3 surfaces
We establish a relationship between mirror symmetry for K3 surfaces and Arnold's strange duality for K3 surfaces. We compute various examples of mirror families. Among them the mirror moduli family for the moduli space of degree 2n polarized K3 surfaces. It turns out to be related to the moduli space of elliptic curves...
1995-02-07
2008-02-03
[ "alg-geom", "hep-th", "math.AG" ]
Igor V. Dolgachev
alg-geom/9502004
Duality of Weights, Mirror Symmetry and Arnold's Strange Duality
A notion of duality of weight systems which corresponds to Batyrev's toric mirror symmetry is given. Explicit duality on the (1,1)-cohomology of K3 surfaces which are minimal models of toric hypersurfaces is constructed using monomial divisor mirror map of Aspinwall-Greene-Morrison. It is shown that Arnold's strange du...
1995-02-06
2008-02-03
[ "alg-geom", "math.AG" ]
Masanori Kobayashi
alg-geom/9502003
A Calabi-Yau threefold with non-Abelian fundamental group
The title is self-explanatory.
1995-02-03
2015-06-30
[ "alg-geom", "math.AG" ]
Arnaud Beauville
alg-geom/9502002
A Generalization of the Kodaira Vanishing and Embedding Theorem
We give several generalizations of the Kodaira vanishing and embedding theorems for K\"ahler manifolds to the case where the relevent line bundle has a small region of negative curvature. To prove the vanishing theorems we adapt techniques of Elworthy-Rosenberg for vanishing theorems in Riemannian geometry. For the emb...
1995-02-02
2015-06-30
[ "alg-geom", "dg-ga", "math.AG", "math.DG" ]
Ying Zhu
alg-geom/9502001
A sextic surface cannot have 66 nodes
Let S be a surface in complex projective 3-space, having only nodes as singularities. Suppose that S has degree 6. We show that the maximum number of nodes which S can have is 65. An abbreviated history of this is as follows. Basset showed that S can have at most 66 nodes. Catanese and Ceresa and Stagnaro constructed...
1995-02-01
2008-02-03
[ "alg-geom", "math.AG" ]
David B. Jaffe and Daniel Ruberman
alg-geom/9501013
The motive of some moduli spaces of vector bundles over a curve
We study the motive of the moduli spaces of semistable rank two vector bundles over an algebraic curve. When the degree is odd the moduli space is a smooth projective variety, we obtain the absolute Hodge motive of this, and in particular the Hodge-Poincare polynomial. When the degree is even the moduli space is a sing...
1995-01-31
2015-06-30
[ "alg-geom", "math.AG" ]
Sebastian del Bano Rollin
alg-geom/9501010
On the tautological ring of $\M _g$
We prove among other things that any product of tautological classes of $\M_g$ of degree $d$ (in the Chow ring of $\M _g$ with rational coefficients) vanishes for $d>g-2$ and is proportional to the class of the hyperelliptic locus in degree $g-2$.
1995-01-20
2015-06-30
[ "alg-geom", "math.AG" ]
Eduard Looijenga
alg-geom/9501011
Some homogeneous coordinate rings that are Koszul algebras
Using reduction to positive characteristic and the method of Frobenius splitting of diagonals, due to Mehta and Ramanathan, it is shown that homogeneous coordinate rings for either proper and smooth toric varieties or Schubert varieties are Koszul algebras.
1995-01-20
2008-02-03
[ "alg-geom", "math.AG" ]
Rikard B\"ogvad
alg-geom/9501012
On the homogeneous ideal of a projective nonsingular toric variety
Reason for withdrawal: There is a serious mistake in the calculation of the divisor of the rational section used in the proof of Prop. 2.2.1., and with the correct value the argument does not work.
1995-01-20
2008-02-03
[ "alg-geom", "math.AG" ]
Rikard B\"ogvad
alg-geom/9501007
Plane Curves with Hyperbolic and C-hyperbolic Complements
The general problem which initiated this work is: What are the quasiprojective varieties which can be uniformized by means of bounded domains in $\cz^n$ ? Such a variety should be, in particular, C--hyperbolic, i.e. it should have a Carath\'{e}odory hyperbolic covering. We study here the plane projective curves who...
1995-01-17
2014-12-02
[ "alg-geom", "math.AG" ]
Gerd Dethloff and Mikhail Zaidenberg
alg-geom/9501009
On the Hilbert scheme of curves in higher-dimensional projective space
In this paper we prove that, for any $n\ge 3$, there exist infinitely many $r\in \N$ and for each of them a smooth, connected curve $C_r$ in $\P^r$ such that $C_r$ lies on exactly $n$ irreducible components of the Hilbert scheme $\hilb(\P^r)$. This is proven by reducing the problem to an analogous statement for the mod...
1995-01-17
2015-06-30
[ "alg-geom", "math.AG" ]
Barbara Fantechi and Rita Pardini
alg-geom/9501008
Quantum cohomology of complete intersections
The quantum cohomology algebra of a projective manifold X is the cohomology H(X,Q) endowed with a different algebra structure, which takes into account the geometry of rational curves in X. We show that this algebra takes a remarkably simple form for complete intersections when the dimension is large enough w.r.t. the ...
1995-01-17
2015-06-30
[ "alg-geom", "math.AG" ]
Arnaud Beauville
alg-geom/9501006
Boundary behaviour of Hurwitz schemes
Actions of finite groups on stable curves are studied. They appear naturally at the boundary of a moduli space of smooth curves with group actions. Those actions which can equivariantly smoothed are characterised. A description of topological types of those actions in terms of the quotient curve and mappings from a kin...
1995-01-16
2015-06-30
[ "alg-geom", "math.AG" ]
Torsten Ekedahl
alg-geom/9501005
An improved bound for the degree of smooth surfaces in P4 not of general type.
This is an addendum to the paper of Braun and Fl{\o}ystad ([BF]) on the bound for the degree of a smooth surface in $\pfour$ not of general type. Using their construction and the regularity of curves in $\pthree$, one may lower the bound a little more. We will prove the following: Theorem. Let $S$ be a smooth surface...
1995-01-16
2015-06-30
[ "alg-geom", "math.AG" ]
Michele Cook
alg-geom/9501004
${\bf C}^*$-extensions of tori, higher Chow groups and applications to incidence equivalence relations for algebraic cycles.
Let X be a smooth projective variety of dimension n. If $p+q=n+1$ then Bloch has defined a ${\bf G}_m$-biextension E over the product of the Chow groups $CH^p_0(X)$ and $CH^q_0(X)$ of homologically trivial cycles. We prove that E is the pullback of the Poincare biextension over the product of intermediate Jacobians in ...
1995-01-10
2014-10-24
[ "alg-geom", "math.AG" ]
Stefan M\"uller-Stach
alg-geom/9501003
Moduli of curves with non-abelian level structure
Following Deligne and Mumford we construct a coarse moduli space of smooth curves with non-abelian level structure, involving higher order commutators. We prove that its Deligne-Mumford compactification is smooth over an open part of Spec(${\msy Z}$).
1995-01-09
2015-06-30
[ "alg-geom", "math.AG" ]
Martin Pikaart and Johan de Jong
alg-geom/9501002
Remarks on the Obstructedness of Cones Over Curves of Low Genus
Remarks on the Obstructedness of Cones Over Curves of Low Genus. Reason for replacement: proof of the main lemma was significantly improved.
1995-01-06
2008-02-03
[ "alg-geom", "math.AG" ]
Ciro Ciliberto, Angelo Lopez, and Rick Miranda