id
large_stringlengths
9
16
title
large_stringlengths
1
382
abstract
large_stringlengths
3
6.09k
publish_date
date32
update_date
date32
categories
large listlengths
1
13
authors
large_stringlengths
3
62.8k
alg-geom/9410007
Flips of moduli spaces and transition formulas for Donaldson polynomial invariants of rational surfaces
We study the change of moduli spaces of Gieseker-semistable torsion free rank-$2$ sheaves on algebraic surfaces as we vary the polarizations. When the surfaces are rational with an effective anti-canonical divisor, the moduli spaces are linked by a series of flips (blowups and blowdowns). Using these results, we comput...
1994-10-12
2008-02-03
[ "alg-geom", "math.AG", "math.GT" ]
Robert Friedman and Zhenbo Qin
alg-geom/9410010
Functorial structure of units in a tensor product
We study the units in a tensor product of rings. For example, let k be an algebraically closed field. Let A and B be reduced rings containing k, having connected spectra. Let u \in A tensor_k B be a unit. Then u = a tensor_k b for some units a \in A and b \in B. Here is a deeper result, stated for simplicity in the aff...
1994-10-12
2008-02-03
[ "alg-geom", "math.AG" ]
David B. Jaffe
alg-geom/9410011
Ample Line Bundles on Blown Up Surfaces
Given a smooth complex projective surface $S$ and an ample divisor $H$ on $S$, consider the blow up of $S$ along $k$ points in general position. Let $H'$ be the pullback of $H$ and $E_1,..., E_k$ be the exceptional divisors. We show that $L = nH' -E_1 - ... -E_k$ is ample if and only if $L^2$ is positive provided the i...
1994-10-12
2008-02-03
[ "alg-geom", "math.AG" ]
Oliver K\"uchle
alg-geom/9410008
Applications of iterated curve blowup to set-theoretic complete intersections in P3
Let S, T be surfaces in P3. Suppose that S intersect T is set-theoretically a smooth curve C of degree d and genus g. Suppose that S and T have no common singular points. Then if C is not a complete intersection, then deg(S), deg(T) < 2d^4. Fixing (d,g), one can form a finite (shorter) list of all possible pairs (deg(S...
1994-10-12
2008-02-03
[ "alg-geom", "math.AG" ]
David B. Jaffe
alg-geom/9410009
Coherent functors, with application to torsion in the Picard group
Let A be a commutative noetherian ring. Call a functor <<commutative A-algebras>> --> <<sets>> coherent if it can be built up (via iterated finite limits) from functors of the form B \mapsto M tensor_A B, where M is a f.g. A-module. When such a functor F in fact takes its values in <<abelian groups>>, we show that ther...
1994-10-12
2015-06-30
[ "alg-geom", "math.AG" ]
David B. Jaffe
alg-geom/9410006
Automorphisms and moduli spaces of varieties with ample canonical class via deformations of abelian covers
By a recent result of Viehweg, projective manifolds with ample canonical class have a coarse moduli space, which is a union of quasiprojective varieties. In this paper, we prove that there are manifolds with ample canonical class that lie on arbitrarily many irreducible components of the moduli; moreover, for any finit...
1994-10-11
2008-02-03
[ "alg-geom", "math.AG" ]
Barbara Fantechi, Rita Pardini
alg-geom/9410005
Variation of moduli spaces and Donaldson invariants under change of polarization
The paper determines the change of moduli spaces of rank $2$ sheaves on surfaces with $p_g=0$ under change of polarization and the corresponding change of the Donaldson invariants. In this revised version we have made some minor stylistic changes in the previous text. In addition we have added a final chapter of about ...
1994-10-07
2008-02-03
[ "alg-geom", "math.AG" ]
Geir Ellingsrud and Lothar G\"ottsche
alg-geom/9410004
Moduli of high rank Vector bundles over Surface
This is the revised version of our previous preprint. In this paper, we establish a generic smoothness result for moduli space of semistable sheaves of arbitrary rank over surfaces provided that the second Chern class of the sheaves is sufficiently large. The theorem is proved using degeneration theory.
1994-10-06
2008-02-03
[ "alg-geom", "math.AG" ]
David Gieseker and Jun Li
alg-geom/9410003
Moduli spaces $M_{g,n}(W)$ for surfaces
We construct and prove the projectiveness of the moduli spaces which are natural generalizations to the case of surfaces of the following: 1) $M_{g,n}$, the moduli space of $n$-marked stable curves, 2) $M_{g,n}(W)$, the moduli space of $n$-marked stable maps to a variety $W$.
1994-10-05
2015-06-30
[ "alg-geom", "math.AG" ]
Valery Alexeev
alg-geom/9410002
Topology of Conjugate Varieties
Serre and Abelson have produced examples of non-homeomorphic conjugate varieties. We show that if the field of definition of a polarized projective variety coincides with its field of moduli then all of its conjugates have the same topological type. This extends the class of varieties known to posses conjugacy invarian...
1994-10-05
2008-02-03
[ "alg-geom", "math.AG" ]
David Reed
alg-geom/9410001
Strong McKay Correspondence, String-theoretic Hodge Numbers and Mirror Symmetry
In the revised version of the paper, we correct misprints and add some new statements.
1994-10-04
2008-02-03
[ "alg-geom", "hep-th", "math.AG" ]
Victor V. Batyrev and Dimitrios I. Dais
alg-geom/9409008
Chamber structure of polarizations and the moduli of stable sheaves on a ruled surface
In this paper we shall generalize the chamber structure of polarizations defined by Qin, and as an application we shall compute the Picard groups of moduli spaces of stable sheaves on a non-rational ruled surface.
1994-10-01
2016-08-14
[ "alg-geom", "math.AG" ]
K\=ota Yoshioka
alg-geom/9409006
Counting twisted cubic curves on general complete intersections
This paper has been rendered obsolete by our newer eprint alg-geom/9411005 "Bott's formula and enumerative geometry", which is a considerably expanded version of the same paper, in spite of the change of titles. Please download alg-geom/9411005 instead, and update possible references.
1994-09-29
2012-01-20
[ "alg-geom", "math.AG" ]
G. Ellingsrud and S. A. Str{\o}mme
alg-geom/9409007
Semistable sheaves on Del Pezzo surfaces and Kronecker modules
In this paper we deal with semistable sheaves which can be represented as the cokernel of an injective (or as the kernel of a surjective) morphism $E_1\otimes\CC^m\longrightarrow E_2\otimes\CC^n$ , where $E_1$ and $E_2$ are exceptional bundles. To each such a sheaf we assign the linear map $\CC^m\otimes\hom^*(E_1,E_2)\...
1994-09-29
2015-06-30
[ "alg-geom", "math.AG" ]
B.V.Karpov
alg-geom/9409005
Non-symmetric orthogonal geometry of Grothendieck rings of coherent sheaves on projective spaces
In this paper we consider orthogonal geometry of the free $\protect\ZZ$-module $K_0(\protect\PP_n)$ with respect to the non-symmetric unimodular bilinear form $$\chi(E,F)=\sum (-1)^\nu\dim\ext^\nu(E,F). $$ We calculate the isometry group of this form and describe invariants of its natural action on $K_0(\protect\PP_n)$...
1994-09-27
2008-02-03
[ "alg-geom", "math.AG" ]
A.L.Gorodentsev
alg-geom/9409004
Riemann reciprocity in higher dimensions
The reciprocity law for abelian differentials of first and second kind is generalized to higher-dimensional varieties. It is shown that $H^1(V)$ of a polarized variety $V$ is encoded in the Laurent data along a curve germ in $V$, with the polarization form on $H^1(V)$ corresponding to the {\em one-dimensional} residue ...
1994-09-09
2008-02-03
[ "alg-geom", "math.AG" ]
Yakov Karpishpan
alg-geom/9409003
Variation of the Gieseker and Uhlenbeck Compactifications
In this article, we study the variation of the Gieseker and Uhlenbeck compactifications of the moduli spaces of Mumford-Takemoto stable vector bundles of rank 2 by changing polarizations. Some {\it canonical} rational morphisms among the Gieseker compactifications are proved to exist and their fibers are studied. As a ...
1994-09-09
2008-02-03
[ "alg-geom", "math.AG" ]
Yi Hu and Wei-Ping Li
alg-geom/9409002
Dynkin Graphs and Triangle Singularities
We treat nine of fourteen triangle singularities in Arnold's classification list of singularities. We consider what kind of combinations of rational double points can appear on their small deformation fibers. We show their combinations are described by a simple priciple using Dynkin graphs.
1994-09-03
2008-02-03
[ "alg-geom", "math.AG" ]
Tohsuke Urabe
alg-geom/9409001
The Number of Rational Quartics on Calabi-Yau hypersurfaces in Weighted Projective Space P(2,1^4)
We compute the number of rational quartics on a general Calabi-Yau hypersurface in weighted projective space P(2,1^4). The result agrees with the prediction made by mirror symmetry.
1994-09-02
2008-02-03
[ "alg-geom", "math.AG" ]
Paul Meurer
alg-geom/9408011
Lectures on Linear Series
The past decade has witnessed two important new developments in the study of linear series on algebraic varieties. First, vector bundles have emerged as powerful tools for analyzing linear series on curves and surfaces. More recently, the viewpoints and techniques of higher dimensional geometry have started to play a c...
1994-08-31
2008-02-03
[ "alg-geom", "math.AG" ]
Robert Lazarsfeld
alg-geom/9408009
Ternary quartics and 3-dimensional commutative algebras
We find the connection between 3-dimensional commutative algebras with a trivial trace and plane quartics and its bitangents.
1994-08-30
2008-02-03
[ "alg-geom", "math.AG" ]
P.Katsylo and D.Mikhailov
alg-geom/9408010
Rationality of the Moduli Variety of Curves of Genus 3
We prove rationality of the moduli variety of curves of genus 3.
1994-08-30
2008-02-03
[ "alg-geom", "math.AG" ]
P.Katsylo
alg-geom/9408008
Various Notions of Associated Prime Ideals
Three notions of associated prime ideals, which are equivalent in the noetherian case but differ in the non notherian case, are discussed. Examples illustrate the scope of the notions.
1994-08-29
2008-02-03
[ "alg-geom", "math.AG" ]
Robert W. Berger
alg-geom/9408006
On Landsberg's criterion for complete intersections
In his preprint ``Differential-Geometric Characterizations of Complete Intersections'' (alg-geom/9407002), J.M.Landsberg introduces an elementary characterization of complete intersections. The proof of this criterion uses the method of moving frames. The aim of this note is to present an elementary proof of Landsberg'...
1994-08-24
2008-02-03
[ "alg-geom", "math.AG" ]
S.L'vovsky
alg-geom/9408007
A surface of general type with \( p_g =q =0, K^2 =1 \)
We construct a surface of general type with invariants \( \chi = K^2 = 1 \) and torsion group \( \Bbb{Z}/{2} \). We use a double plane construction by finding a plane curve with certain singularities, resolving these, and taking the double cover branched along the resulting smooth curve.
1994-08-24
2008-02-03
[ "alg-geom", "math.AG" ]
Caryn Werner
alg-geom/9408005
Moduli of Brill-Noether pairs on algebraic curves
We construct coarse moduli spaces for `Brill-Noether pairs'. Such a pair consists of a torsion-free sheaf $E$ over an algebraic curve $X$ and a vector subspace $\Lambda$ of its space of sections $H^0(E)$. The construction works for an arbitrary singular curve $X$ of pure dimension and for all values of the positive rat...
1994-08-10
2008-02-03
[ "alg-geom", "math.AG" ]
A.D. King and P.E. Newstead
alg-geom/9408004
Cubics, Integrable Systems, and Calabi-Yau Threefolds
In this work we construct an analytically completely integrable Hamiltonian system which is canonically associated to any family of Calabi-Yau threefolds. The base of this system is a moduli space of gauged Calabi-Yaus in the family, and the fibers are Deligne cohomology groups (or intermediate Jacobians) of the threef...
1994-08-09
2008-02-03
[ "alg-geom", "math.AG" ]
Ron Donagi and Eyal Markman
alg-geom/9408003
Local Positivity of Ample Line Bundles
Let $L$ be a nef line bundle on a smooth complex projective variety $X$ of dimension $n$. Demailly has introduced a very interesting invariant --- the Seshadri constant $\epsilon(L,x)$ --- which in effect measures how positive $L$ is locally near a given point $x \in X$. For instance, Seshadri's criterion for ampleness...
1994-08-09
2008-02-03
[ "alg-geom", "math.AG" ]
Lawrence Ein, Oliver K\"uchle and Robert Lazarsfeld
alg-geom/9408002
${\cal H}$-cohomologies versus algebraic cycles
Global intersection theories for smooth algebraic varieties via products in {\it appropriate}\, Poincar\'e duality theories are obtained. We assume given a (twisted) cohomology theory $H^*$ having a cup product structure and we let consider the ${\cal H}$-cohomology functor $X\leadsto H^{\#}_{Zar}(X,{\cal H}^*)$ where ...
1994-08-08
2008-02-03
[ "alg-geom", "math.AG" ]
Luca Barbieri-Viale
alg-geom/9408001
Hodge numbers of moduli spaces of stable bundles on K3 surfaces
We show that the Hodge numbers of the moduli space of stable rank two sheaves with primitive determinant on a K3 surface coincide with the Hodge numbers of an appropriate Hilbert scheme of points on the K3 surface. The precise result is: Theorem: Let $X$ be a K3 surface, $L$ a primitive big and nef line bundle and $H$ ...
1994-08-04
2008-02-03
[ "alg-geom", "math.AG" ]
Lothar Goettsche, Daniel Huybrechts
alg-geom/9407012
On certain N--sheeted coverings and numerical semigroups which cannot be realized as Weierstrass semigroups
A curve $X$ is said to be of type $(N,\gamma)$ if it is an $N$--sheeted covering of a curve of genus $\gamma$ with at least one totally ramified point. A numerical semigroup $H$ is said to be of type $(N,\gamma)$ if it has $\gamma$ positive multiples of $N$ in $[N,2N\gamma]$ such that its $\gamma^{th}$ element is $2N\g...
1994-07-26
2008-02-03
[ "alg-geom", "math.AG" ]
Fernando Torres
alg-geom/9407011
Complex monodromy and the topology of real algebraic sets
We study the Euler characteristic of the real Milnor fibres of a real analytic map, using a relation between complex monodromy and complex conjugation. We deduce the result of Coste and Kurdyka that the Euler characteristic of the link of an irreducible algebraic subset of a real algebraic set is generically constant m...
1994-07-19
2008-02-03
[ "alg-geom", "math.AG" ]
Clint McCrory and Adam Parusinski
alg-geom/9407010
Real Grassmann Polylogarithms and Chern Classes
In this paper we define real grassmann polylogarithms, which are real single valued analogues of the grassmann polylogarithms (or higher logarithms) defined by Hain and MacPherson. We prove the existence of all such real grassmann polylogs, at least generically. We also prove that the canonical choice of such an m-poly...
1994-07-18
2008-02-03
[ "alg-geom", "math.AG" ]
Richard Hain and Jun Yang
alg-geom/9407009
Mordell-Weil problem for cubic surfaces
Drawing the secant through two rational points of a cubic surface we can get the third one. Is the set of rational points finitely generated? We discuss some numerical data and prove a finite generation statement with respect to a modified composition law.
1994-07-15
2008-02-03
[ "alg-geom", "math.AG" ]
Yu.I.Manin
alg-geom/9407007
Beyond the K\"ahler cone
The moduli space of nonlinear $\sigma$-models on a Calabi--Yau manifold contains a complexification of the K\"ahler cone of the manifold. We describe a physically natural analytic continuation process which links the complexified K\"ahler cones of birationally equivalent Calabi--Yau manifolds. The enlarged moduli space...
1994-07-14
2008-02-03
[ "alg-geom", "math.AG" ]
David R. Morrison
alg-geom/9407008
Natural transformations from constructible functions to homology
For complex projective varieties, all natural transformations from constructible functions to homology (modulo torsion) are linear combinations of the MacPherson-Schwartz-Chern classes. (The authors are willing to mail hard copies of the paper.)
1994-07-14
2008-02-03
[ "alg-geom", "math.AG" ]
Gary Kennedy, Clint McCrory, and Shoji Yokura
alg-geom/9407006
Reduction of the Manin map modulo $p$
For an abelian variety $A$ over a function field $K$ of characteristic zero, Manin defined a remarkable additive map $A(K) \ra V$, where $V$ is a vector space over $K$. We define an analogue of this map in the case of function fields of characteristic $p$. We then prove that the reduction modulo $p$ of the Manin map in...
1994-07-13
2008-02-03
[ "alg-geom", "math.AG" ]
A. Buium and J.F. Voloch
alg-geom/9407005
Generating Functions in Algebraic Geometry and Sums over Trees
We calculate generating functions for the Poincare polynomials of moduli spaces of pointed curves of genus zero and of Configuration Spaces of Fulton and MacPherson. We also prove that contributions of multiple coverings of curves in a Calabi-Yau threefold calculated via Kontsevich's compactification coincide with the ...
1994-07-12
2008-02-03
[ "alg-geom", "math.AG" ]
Yu. I. Manin
alg-geom/9407004
On the stability of the tangent bundle of Fano manifolds
By using the classification of Fano 3-folds we prove: Let $X$ be Fano 3-fold. Assume that the tangent bundle $T_X$ of $X$ is not stable (i.e. semi-stable or unstable). Then $b_2\geq 2$ and a relative tangent sheaf $T_{X/Y}$ of a contraction $f:X\longrightarrow Y$ of an extremal face on $X$ is a destabilising subsheaf o...
1994-07-10
2008-02-03
[ "alg-geom", "math.AG" ]
Andreas Steffens
alg-geom/9407003
Canonical Generators for the Cohomology of Moduli of Parabolic Bundles on Curves
We determine generators of the rational cohomology algebras of moduli spaces of parabolic vector bundles on a curve, under some `primality' conditions on the parabolic datum. These generators are canonical in a precise sense. Our results are new even for usual vector bundles (i.e., vector bundles without parabolic stru...
1994-07-04
2008-02-03
[ "alg-geom", "math.AG" ]
I.Biswas and N.Raghavendra
alg-geom/9407001
Quadrature Mirror Filters and Loop Groups
In this paper we want to show, that the finite impulse response quadratic mirror filters (QMF) associated to a tower of grids $\Gamma\subset H=\bf Z^n$ can be identified with a right coset of the subgroup Fix$(T_{\Gamma^{\perp}}$,Map$ ({\bf T}^n\to U(N)$: poly) of the group of polynomial loops Map$({\bf T}^n\to U(N)$: ...
1994-07-01
2008-02-03
[ "alg-geom", "math.AG" ]
Matthias Holschneider
alg-geom/9407002
Differential-geometric characterizations of complete intersections
The exposition has been significantly altered, hopefully improved.
1994-07-01
2008-02-03
[ "alg-geom", "dg-ga", "math.AG", "math.DG" ]
J.M. Landsberg
alg-geom/9406008
Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves
Based on the combinatorial description of the moduli spaces of curves provided by Strebel differentials, Witten and Kontsevich have introduced combinatorial cohomology classes $W_{(m_0,m_1,m_2,\dots),n}$, and conjectured that these can be expressed in terms of Mumford-Morita-Miller classes. It is argued that this link ...
1994-06-30
2015-06-30
[ "alg-geom", "hep-th", "math.AG" ]
Enrico Arbarello and Maurizio Cornalba
alg-geom/9406007
Some glueing formulas for spin polynomials and a proof of the Van de Ven conjecture
We deduce some formulas for the spin invariants of the connected sum of an arbitrary 4-manifold X, b^+ _2(X) > 0 $ with $\overline {CP^2}$ in terms of the spin invariants of $X$ and apply this to prove the Van de Ven conjecture.
1994-06-27
2008-02-03
[ "alg-geom", "math.AG" ]
Victor Pidstrigatch
alg-geom/9406006
Infinite-dimensional Lie algebras and the period map for curves
We compute higher-order differentials of the period map for curves and show how they factor through the corresponding higher Kodaira-Spencer classes. Our approach is based on the infinitesimal equivariance of the period map, due to Arbarello and De Concini \cite{AD}.
1994-06-23
2008-02-03
[ "alg-geom", "math.AG" ]
Yakov Karpishpan
alg-geom/9406005
Pfaffian Subschemes
A subscheme $X\subset \Bbb P^{n+3}$ of codimension $3$ is {\em Pfaffian} if it is the degeneracy locus of a skew-symmetric map $f:\cal{E}\spcheck(-t) @>>> \cal{E}$ with $\cal{E}$ a locally free sheaf of odd rank on $\Bbb P^{n+3}$. It is shown that a codimension $3$ subscheme $X\subset\Bbb P^{n+3}$ is Pfaffian if and on...
1994-06-17
2008-02-03
[ "alg-geom", "math.AG" ]
Charles H. Walter
alg-geom/9406003
Universal Hodge Bundle and Mumford Isomorphisms on the Abelian Inductive Limit of Teichm\"uller Spaces
Let $\Mg$ denote the moduli space of compact Riemann surfaces of genus $g$. Mumford had proved that, for each fixed genus $g$, there are isomorphisms asserting that certain higher $DET$ bundles over $\Mg$ are certain fixed (genus-independent) tensor powers of the Hodge line bundle on $\Mg$. Here we obtain a coherent, g...
1994-06-15
2008-02-03
[ "alg-geom", "hep-th", "math.AG" ]
Indranil Biswas, Subhashis Nag and Dennis Sullivan
alg-geom/9406004
Log Smooth Deformation Theory
This paper gives a foundation of log smooth deformation theory. We study the infinitesimal liftings of log smooth morphisms and show that the log smooth deformation functor has a representable hull. This deformation theory gives, for example, the following two types of deformations: (1) relative deformations of a certa...
1994-06-15
2008-02-03
[ "alg-geom", "math.AG" ]
Fumiharu Kato
alg-geom/9406002
Spin canonical invariants of 4-manifolds and algebraic surfaces
The paper is a colloquial-style discussion of invariants of algebraic surfaces analogous to the Donaldson polynomials, arising from moduli spaces of ``jumping'' Yang--Mills instantons, or moduli spaces of jumping vector bundles. The invariants have the following applications: (1) to the Van de Ven conjecture that the K...
1994-06-13
2008-02-03
[ "alg-geom", "math.AG" ]
Andrei Tyurin
alg-geom/9406001
Gorenstein Quotient Singularities of Monomial Type in Dimension Three
The purpose of this paper is to construct a crepant resolution of quotient singularities by finite subgroups of SL(3,C) of monomial type, and prove that the Euler number of the resolution is equal to the number of conjugacy classes. This result is a part of conjecture II in previous paper "Crepant resolution of trihedr...
1994-06-11
2008-02-03
[ "alg-geom", "math.AG" ]
Yukari Ito
alg-geom/9405014
On Riemann-Roch Formulas for Multiplicities
A Theorem due to Guillemin and Sternberg about geometric quantization of Hamiltonian actions of compact Lie groups $G$ on compact Kaehler manifolds says that the dimension of the $G$-invariant subspace is equal to the Riemann-Roch number of the symplectically reduced space. Combined with the shifting-trick, this gives ...
1994-05-30
2008-02-03
[ "alg-geom", "math.AG" ]
Eckhard Meinrenken
alg-geom/9405013
Deformation theory and Lie algebra homology
A description of a ring of functions on the base of a universal formal deformation for several moduli problems is given. The answer is given in terms of a homology group of a certain dg Lie algebra canonically (up to an essentially unique quasi-isomorphism) associated with a problem.
1994-05-25
2008-02-03
[ "alg-geom", "hep-th", "math.AG" ]
Vladimir Hinich and Vadim Schechtman
alg-geom/9405012
Local structure of the moduli space of vector bundles over curves
We analyze the local structure of the moduli space of semi-stable bundles on a curve. In particular, a complete description of the local structure is given in the rank 2 case. We obtain as a corollary of this analysis new results about the Kummer variety and the Coble quartic associated to a canonical genus 3 curve.
1994-05-24
2008-02-03
[ "alg-geom", "math.AG" ]
Yves Laszlo
alg-geom/9405011
Algebraic Surfaces with Log-Terminal Singularities and nef Anticanonical Class and Reflection Groups in Lobachevsky Spaces. I (Basics of the Diagram Method)
In our preprint: "Algebraic surfaces with log-terminal singularities and nef anticanonical class and reflection groups in Lobachevsky spaces", Preprint Max-Planck-Institut f\"ur Mathematik, Bonn, (1989) MPI/89-28 (Russian), we had extended the diagram method to algebraic surfaces with nef anticanonical class (before, i...
1994-05-23
2008-02-03
[ "alg-geom", "math.AG" ]
Viacheslav V. Nikulin
alg-geom/9405009
Some properties of Fano manifolds that are zeros of sections in homogenous vector bundles over Grassmannians
Let $X$ be a Fano manifold which is the zero scheme of a general global section $s$ in an irreducible homogenous vector bundle over a Grassmannian. We prove that the restriction of the Pl\"ucker embedding embeds $X$ projectively normal, and that every small deformation of $X$ comes from a deformation of the section $s$...
1994-05-20
2008-02-03
[ "alg-geom", "math.AG" ]
Oliver K\"uchle
alg-geom/9405010
Adjoints of ideals in regular local rings
The adjoint of an ideal I in a regular local ring R is the R-ideal adj(I):=H^0(Y, I\omega_Y), where f:Y -> Spec(R) is a proper birational map with Y nonsingular and IO_Y invertible, and \omega_f is a canonical relative dualizing sheaf. (Such an f is supposed to exist.) The basic conjecture is that I.adj(I^n)=adj(I^{n+1...
1994-05-20
2008-02-03
[ "alg-geom", "math.AC", "math.AG" ]
Joseph Lipman
alg-geom/9405008
Infinitesimal Deformations and Obstructions for Toric Singularities
The obstruction space T^2 and the cup product T^1 x T^1 -> T^2 are computed for toric singularities.
1994-05-16
2008-02-03
[ "alg-geom", "math.AG" ]
Klaus Altmann
alg-geom/9405007
On the A-D-E classification of the simple singularities of functions
We show how the classification of simple singularities of functions can be reduced directly, not using the normal forms, to the classification of irreducible Weyl groups. We also prove that the class of a singularity in its local algebra always belongs to the tangent cone to the stratum $\mu =const$ of the singularity....
1994-05-15
2008-02-03
[ "alg-geom", "math.AG" ]
Mikhail Entov
alg-geom/9405006
A Fourier-Mukai Transform for Stable Bundles on K3 Surfaces
We define a Fourier-Mukai transform for sheaves on K3 surfaces over $\C$, and show that it maps polystable bundles to polystable ones. The role of ``dual'' variety to the given K3 surface $X$ is here played by a suitable component $\hat X$ of the moduli space of stable sheaves on $X$. For a wide class of K3 surfaces $\...
1994-05-13
2008-02-03
[ "alg-geom", "math.AG" ]
C. Bartocci, U. Bruzzo, and D. Hernandez Ruiperez
alg-geom/9405005
Higher-order differentials of the period map and higher Kodaira-Spencer classes
In \cite{K} we introduced two variants of higher-order differentials of the period map and showed how to compute them for a variation of Hodge structure that comes from a deformation of a compact K\"ahler manifold. More recently there appeared several works (\cite{BG}, \cite{EV}, \cite{R}) defining higher tangent space...
1994-05-12
2008-02-03
[ "alg-geom", "math.AG" ]
Yakov Karpishpan
alg-geom/9405004
Geometric invariant theory and flips
We study the dependence of geometric invariant theory quotients on the choice of a linearization. We show that, in good cases, two such quotients are related by a flip in the sense of Mori, and explain the relationship with the minimal model programme. Moreover, we express the flip as the blow-up and blow-down of speci...
1994-05-10
2008-02-03
[ "alg-geom", "math.AG" ]
Michael Thaddeus
alg-geom/9405003
An Algorithmic Proof of Suslin's Stability Theorem over Polynomial Rings
Let $k$ be a field. Then Gaussian elimination over $k$ and the Euclidean division algorithm for the univariate polynomial ring $k[x]$ allow us to write any matrix in $SL_n(k)$ or $SL_n(k[x])$, $n\geq 2$, as a product of elementary matrices. Suslin's stability theorem states that the same is true for the multivariate po...
1994-05-10
2008-02-03
[ "alg-geom", "math.AG" ]
H. Park and C. Woodburn
alg-geom/9405002
The blowup formula for Donaldson invariants
In this paper we present a formula which relates the Donaldson invariants of a 4-manifold X with the Donaldson invariants of its blowup X#-CP(2). This blow-up formula is independent of X and involves sigma-functions associated to a naturally arising elliptic function. This, the final version, corrects some earlier misc...
1994-05-09
2008-02-03
[ "alg-geom", "math.AG" ]
Ronald Fintushel and Ronald Stern
alg-geom/9405001
Conformal blocks, fusion rules and the Verlinde formula
The Verlinde formula computes the dimension of certain vector spaces ("conformal blocks") associated to a Rational Conformal Field Theory. In this paper we show how this can be made rigorous for one particular such theory, the WZW model. Thanks to the results of [B-L], [F] and [T-U-Y], this gives the dimension of the s...
1994-05-05
2008-02-03
[ "alg-geom", "math.AG" ]
A. Beauville
alg-geom/9404014
Basic cohomology of associative algebras
We define a new cohomology for associative algebras which we compute for algebras with units.
1994-04-28
2010-04-01
[ "alg-geom", "math.AG" ]
Michel Dubois-Violette and Thierry Masson
alg-geom/9404012
Group cohomology construction of the cohomology of moduli spaces of flat connections on 2-manifolds
We use group cohomology and the de Rham complex on simplicial manifolds to give explicit differential forms representing generators of the cohomology rings of moduli spaces of representations of fundamental groups of 2-manifolds. These generators are constructed using the de Rham representatives for the cohomology of c...
1994-04-28
2008-02-03
[ "alg-geom", "hep-th", "math.AG" ]
Lisa C. Jeffrey
alg-geom/9404013
Symplectic Forms on Moduli Spaces of Flat Connections on 2-manifolds
Let $G$ be a compact connected semisimple Lie group. We extend the techniques of Weinstein [W] to give a construction in group cohomology of symplectic forms $\omega$ on \lq twisted' moduli spaces of representations of the fundamental group $\pi$ of a 2-manifold $\Sigma$ (the smooth analogues of ${\rm Hom} (\pi_1(\Sigm...
1994-04-28
2008-02-03
[ "alg-geom", "hep-th", "math.AG" ]
Lisa C. Jeffrey
alg-geom/9404011
Computing Multidimensional Residues
Given n polynomials in n variables with a finite number of complex roots, for any of their roots there is a local residue operator assigning a complex number to any polynomial. This is an algebraic, but generally not rational, function of the coefficients. On the other hand, the global residue, which is the sum of the ...
1994-04-27
2015-06-30
[ "alg-geom", "math.AG" ]
Eduardo Cattani, Alicia Dickenstein, Bernd Sturmfels
alg-geom/9404010
On complex surfaces diffeomorphic to rational surfaces
In this paper we prove that no complex surface of general type is diffeomorphic to a rational surface, thereby completing the smooth classification of rational surfaces and the proof of the Van de Ven conjecture on the smooth invariance of Kodaira dimension.
1994-04-22
2009-10-22
[ "alg-geom", "math.AG", "math.GT" ]
Robert Friedman and Zhenbo Qin
alg-geom/9404009
Moduli of abelian surfaces with a $(1,p^2)$ polarisation
We show that the (compactified) moduli space of abelian surfaces with a polarisation of type $(1,p^2)$ is of general type for $p \ge 11$, improving a result of O'Grady.
1994-04-21
2008-02-03
[ "alg-geom", "math.AG" ]
v.A. Gritsenko and G.K. Sankaran
alg-geom/9404008
Crepant resolution of trihedral singularities
The purpose of this paper is to construct a crepant resolution of quotient singularities by trihedral groups ( finite subgroups of SL(3,C) of certain type ), and prove that each Euler number of the minimal model is equal to the number of conjugacy classes. Trihedral singularities are 3-dimensional version of D_n-singul...
1994-04-15
2008-02-03
[ "alg-geom", "math.AG" ]
Yukari Ito
alg-geom/9404006
Degenerations of abelian surfaces and Hodge structures
In this paper the authors consider a certain toroidal compactification of the moduli space of degenerations of (1,p)-polarized abelian surfaces with (canonical) level structure. Using Hodge theory we give a proof that a degenerate abelian surface associated to a corank 1 boundary point is (almost) completely determined...
1994-04-12
2008-02-03
[ "alg-geom", "math.AG" ]
K. Hulek and J. Spandaw
alg-geom/9404007
On the Existence of Supersingular Curves of Given Genus
We give a method to construct explicitly a supersingular curve of given genus g in characteristic 2.
1994-04-12
2008-02-03
[ "alg-geom", "math.AG" ]
Gerard van der Geer and Marcel van der Vlugt
alg-geom/9404005
On curves and surfaces with projectively equivalent hyperplane sections
In this paper we describe projective curves and surfaces such that almost all their hyperplane sections are projectively equivalent. Our description is complete for curves and close to being complete for smooth surfaces. In the appendix we make some remarks on connections between the mentioned property of a projective ...
1994-04-12
2008-02-03
[ "alg-geom", "math.AG" ]
S.L'vovsky
alg-geom/9404004
Moduli of vector bundles on projective surfaces: some basic results
We prove that moduli spaces of torsion-free sheaves on a projective smooth complex surface are irreducible, reduced and of the expected dimension, provided the expected dimension is large enough. Actually we prove more: given a line bundle on the surface, we show that the number of moduli of sheaves which have a non-ze...
1994-04-06
2008-02-03
[ "alg-geom", "math.AG" ]
Kieran G. O'Grady
alg-geom/9404003
Bogomolov unstability on arithmetic surfaces
In this note, we will consider an arithmetic analogue of Bogomolov unstability theorem.
1994-04-05
2008-02-03
[ "alg-geom", "math.AG" ]
Atsushi Moriwaki
alg-geom/9404001
Vector bundles on curves and generalized theta functions: recent results and open problems
Riemann surface carries a natural line bundle, the determinant bundle. The space of sections of this line bundle (or its multiples) constitutes a natural non-abelian generalization of the spaces of theta functions on the Jacobian. There has been much progress in the last few years towards a better understanding of thes...
1994-04-05
2008-02-03
[ "alg-geom", "math.AG" ]
Arnaud Beauville
alg-geom/9404002
Nonnormal del Pezzo surfaces
This paper studies reduced, connected, Gorenstein surfaces with ample -K, assumed to be reducible or nonnormal. The normalisation is a union of one or more standard surfaces (scrolls and Veronese surfaces), marked with a conic as double locus. The question is how to glue these together to get a Gorenstein scheme. In ch...
1994-04-05
2008-02-03
[ "alg-geom", "math.AG" ]
Miles Reid
alg-geom/9403016
Groupe de Picard de la vari\'et\e de modules des th\^eta-caracteristiques des courbes planes
Nous calculons le groupe de Picard de l'espace des modules $\Theta_{\planp}(d)$ des th\^eta-caract\'eristiques des courbes planes (non forc\'ement lisses) de degr\'e $d$. Nous montrons que pour $d\ge 6$, le groupe de Picard de la composante paire est engendr\'e par le fibr\'e d\'eterminant ${\cal{D}}$ et l'image r\'eci...
1994-03-28
2008-02-03
[ "alg-geom", "math.AG" ]
Christoph Sorger
alg-geom/9403015
Torelli Groups and Geometry of Moduli Spaces of Curves
In this paper we give an exposition of Dennis Johnson's work on the first homology of the Torelli groups and show how it can be applied, alone and in concert with Saito's theory of Hodge modules, to study the geometry of moduli spaces of curves. For example, we show that the picard groups of moduli spaces of curves wit...
1994-03-27
2008-02-03
[ "alg-geom", "math.AG" ]
Richard M. Hain
alg-geom/9403014
On Chow Rings of Fine Moduli Spaces of Modules
Let $M$ be a complete nonsingular fine moduli space of modules over an algebra $S$. A set of conditions is given for the Chow ring of $M$ to be generated by the Chern classes of certain universal bundles occurring in a projective resolution of the universal $S$-module on $M$. This result is then applied to the varietie...
1994-03-18
2008-02-03
[ "alg-geom", "math.AG" ]
A. D. King and Charles H. Walter
alg-geom/9403013
Complexes inattendus de droites de saut (Unexpected complex of jumping lines)
We prove here the following results: \begin{th} Let $E$ a rank 2 vector bundle over ${\bf P}_3$, if $C$ is a reduced irreducible curve of ${\bf P}_3^{\vee}$ such that $E_H$ is unstable for all $H\in C$ then $C$ is a line. \end{th} We define now the set $W(E)$ as the set of planes $H$ such that the restricted bundle $...
1994-03-17
2024-12-02
[ "alg-geom", "math.AG" ]
Jean Valles
alg-geom/9403012
Minimal discrepancies of toric singularities
This is the major revision. The main purpose of this paper is to prove that minimal discrepancies of $n$-dimensional toric singularities can accumulate only from above and only to minimal discrepancies of toric singularities of dimension less than $n$. I also prove that some lower-dimensional minimal discrepancies do a...
1994-03-15
2008-02-03
[ "alg-geom", "math.AG" ]
A. Borisov
alg-geom/9403010
On Quantum Cohomology Rings of Fano Manifolds and a Formula of Vafa and Intriligator
We observe a general structure theorem for quantum cohomology rings, a non-homogeneous version of the usual cohomology ring encoding information about (almost holomorphic) rational curves. An application is the rigorous computation of the quantum cohomology of Grassmannians. As purely algebraic consequence we prove a b...
1994-03-12
2008-02-03
[ "alg-geom", "math.AG" ]
Bernd Siebert and Gang Tian
alg-geom/9403011
Hodge index theorem for arithmetic cycles of codimension one
In this note, we will give a partial answer for arithmetic analogues of Grothendieck's standard conjectures due to H. Gillet and C. Soule. (Remark : I changed the title of this note.)
1994-03-12
2008-02-03
[ "alg-geom", "math.AG" ]
Atsushi Moriwaki
alg-geom/9403008
Torus embeddings and algebraic intersection complexes
We describe the intersection complex of any perversity of a toric variety completely in terms of the associated fan. It is described by a finite complex of finite dimensional graded vector spaces which we call graded exterior modules. The intersection complexes of the middle perversity are treated in the second part fo...
1994-03-11
2008-02-03
[ "alg-geom", "math.AG" ]
Masa-Nori Ishida
alg-geom/9403009
Torus embeddings and algebraic intersection complexes, II
In the previous paper, we describe the intersection complexes of a toric variety as a finite complex of graded exterior modules on the associated fan. In this second part, we rewrite it explicitly by the barycentric subdivision of the fan. We get the decomposition theorem of the intersection homologies for a barycentri...
1994-03-11
2008-02-03
[ "alg-geom", "math.AG" ]
Masa-Nori Ishida
alg-geom/9403007
Towards a Schubert calculus for maps from a Riemann surface to a Grassmannian
The intuitive notion of the Gromov invariant for maps from a Riemann surface to a Grassmannian is shown to agree with the definition in \cite{BDW}. Also, an induction on the genus is proved, which extends the results of \cite{BDW} to a computation of all Gromov invariants associated to G(2,k). This is shown to agree wi...
1994-03-10
2008-02-03
[ "alg-geom", "math.AG" ]
Aaron Bertram
alg-geom/9403006
Hyperkaehler Embeddings II
In the first part, Hyperkaehler Embeddings and Holomorphic symplectic Geometry I, we prove the following. Let $N$ be a closed analytic subvariety of a generic deformation of a holomorphically symplectic compact manifold $M$. Then the restriction of a holomorphic symplectic form is non-degenerate on $N$. In particular, ...
1994-03-06
2008-02-03
[ "alg-geom", "math.AG" ]
Misha Verbitsky
alg-geom/9403005
Siegel modular forms generated by invariants of cubic hypersurfaces
We give a geometric derivation of Schottky's equation in genus four for the period matrices of Riemann surfaces among all period matrices. The equation arises naturally from the singularity theory of the Gauss map on the theta divisor, and thus generalizes for any genus $g \ge 4$ to a certain ideal of Siegel modular fo...
1994-03-03
2008-02-03
[ "alg-geom", "math.AG" ]
C. McCrory, T. Shifrin, R. Varley (University of Georgia)
alg-geom/9403003
Toric Q-Gorenstein Singularities
For an affine, toric Q-Gorenstein variety Y (given by a lattice polytope Q) the vector space T^1 of infinitesimal deformations is related to the complexified vector spaces of rational Minkowski summands of faces of Q. Moreover, assuming Y to be an isolated, at least 3-dimensional singularity, Y will be rigid unless it ...
1994-03-02
2008-02-03
[ "alg-geom", "math.AG" ]
Klaus Altmann
alg-geom/9403004
The versal Deformation of an isolated toric Gorenstein Singularity
Given a lattice polytope Q in R^n, we define an affine scheme M(Q) that reflects the possibilities of splitting Q into a Minkowski sum. On the other hand, Q induces a toric Gorenstein singularity Y, and we construct a flat family over M(Q) with Y as special fiber. In case Y has an isolated singularity only, this family...
1994-03-02
2008-02-03
[ "alg-geom", "math.AG" ]
Klaus Altmann
alg-geom/9403001
Residual Intersections and Some Applications
We give a new residual intersection decomposition for the refined intersection products of Fulton-MacPherson. Our formula refines the celebrated residual intersection formula of Fulton, Kleiman, Laksov, and MacPherson. The new decomposition is more likely to be compatible with the canonical decomposition of the interse...
1994-03-01
2008-02-03
[ "alg-geom", "math.AG" ]
Xian Wu
alg-geom/9403002
Intersection Theory on Toric Varieties
The operational Chow cohomology classes of a complete toric variety are identified with certain functions, called Minkowski weights, on the corresponding fan. The natural product of Chow cohomology classes makes the Minkowski weights into a commutative ring; the product is computed by a displacement in the lattice, whi...
1994-03-01
2008-02-03
[ "alg-geom", "math.AG" ]
William Fulton and Bernd Sturmfels
alg-geom/9402014
The Deformation Space of Calabi-Yau n-folds with canonical singularities can be obstructed
This paper gives a simple example of a family of Calabi-Yaus of any dimension with canonical singularities of dimension one, whose Kuranishi space is singular. Thus the Bogomolov-Tian-Todorov unobstructedness theorem is not true for Calabi-Yaus with canonical singularities.
1994-02-25
2008-02-03
[ "alg-geom", "math.AG" ]
Mark Gross
alg-geom/9402013
Faltings modular height and self-intersection of dualizing sheaf
Let K be a number field, O_K the ring of integers of K and X a stable curve over O_K of genus g >= 2. In this note, we will prove a strict inequality ( (K_{X/S})^2 / [K : Q] ) > Height_{Fal}(J(X_K)), where $K_{X/S}$ is the canonically metrized dualizing sheaf of X over S = Spec(O_K) and Height_{Fal}(J(X_K)) is the ...
1994-02-17
2008-02-03
[ "alg-geom", "math.AG" ]
Atsushi Moriwaki
alg-geom/9402012
Factorization theorems for the representations of the fundamental groups of quasiprojective varieties and some applications
In this paper, using Gromov-Jost-Korevaar-Schoen technique of harmonic maps to nonpositively curved targets, we study the representations of the fundamental groups of quasiprojective varieties. As an application of the above considerations we give a proof of a weak version of the Shafarevich Conjecture.
1994-02-16
2008-02-03
[ "alg-geom", "math.AG" ]
Ludmil Katzarkov
alg-geom/9402011
Degree of the generalized Pl\"ucker embedding of a Quot scheme and Quantum cohomology
We compute the degree of the generalized Pl\"ucker embedding $\kappa$ of a Quot scheme $X$ over $\PP^1$. The space $X$ can also be considered as a compactification of the space of algebraic maps of a fixed degree from $\PP^1$ to the Grassmanian $\rm{Grass}(m,n)$. Then the degree of the embedded variety $\kappa (X)$ can...
1994-02-15
2017-01-06
[ "alg-geom", "hep-th", "math.AG" ]
M.S.Ravi, J. Rosenthal and X.Wang
alg-geom/9402010
On Polarized Manifolds of Sectional Genus Three
This paper is an attempt for the classification of polarized manifolds of sectional genus $g=3$ and dimension $n\geq 3$. As in the case of $g\leq 2$,which was classified by T.Fujita,we use Mori-Kawamata theory. The classification result of $g=3$ and $n=2$, which was obtained by H.Maeda,is also used essentially. Althoug...
1994-02-14
2008-02-03
[ "alg-geom", "math.AG" ]
Hironobu Ishihara
alg-geom/9402009
On the Locus of Hodge Classes
Let $f: X \rightarrow S$ be a family of non singular projective varieties parametrized by a complex algebraic variety $S$. Fix $s \in S$, an integer $p$, and a class $h \in {\rm H}^{2p}(X_s,\Z)$ of Hodge type $(p,p)$. We show that the locus, on $S$, where $h$ remains of type $(p,p)$ is algebraic. This result, which in ...
1994-02-10
2008-02-03
[ "alg-geom", "math.AG" ]
Eduardo Cattani, Pierre Deligne, and Aroldo Kaplan