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 |
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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 |
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