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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1995-11-07T06:20:12 | 9511 | alg-geom/9511003 | en | https://arxiv.org/abs/alg-geom/9511003 | [
"alg-geom",
"math.AG"
] | alg-geom/9511003 | Dr. P. E. Newstead | L. Brambila Paz, I. Grzegorczyk, and P. E. Newstead | Geography of Brill-Noether loci for small slopes | 34pp and 3 figures. Figures (not included in e-print) may be obtained
by sending your mailing address to newstead@liv.ac.uk; complete hard copy
also available. LaTeX 2.09 | null | null | null | null | Let $X$ be a non-singular projective curve of genus $g\ge2$ over an
algebraically closed field of characteristic zero. Let $\mo$ denote the moduli
space of stable bundles of rank $n$ and degree $d$ on $X$ and $\wn $ the
Brill-Noether loci in $\mo .$ We prove that, if $0\leq d \leq n $ and $\wn $ is
non-empty, then it... | [
{
"version": "v1",
"created": "Mon, 6 Nov 1995 17:36:29 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Paz",
"L. Brambila",
""
],
[
"Grzegorczyk",
"I.",
""
],
[
"Newstead",
"P. E.",
""
]
] | alg-geom | \section*{Introduction}
\bigskip The moduli spaces of stable vector bundles over
an algebraic curve have been extensively studied from
many points of view since they were first constructed
more than 30 years ago, and much is now known about their
detailed structure, in particular in terms of their
topology. Except ... |
1995-12-04T06:20:14 | 9511 | alg-geom/9511018 | en | https://arxiv.org/abs/alg-geom/9511018 | [
"alg-geom",
"math.AG"
] | alg-geom/9511018 | Alexander Polishchuk | Alexander Polishchuk | Symplectic biextensions and a generalization of the Fourier-Mukai
transform | AMSLaTeX. Missing package "comm" is inserted | null | null | null | null | A generalization of the Fourier-Mukai transform is proposed. The construction
is based on analogy with the classical picture of representations of the
Heisenberg group.
| [
{
"version": "v1",
"created": "Tue, 28 Nov 1995 18:32:30 GMT"
},
{
"version": "v2",
"created": "Fri, 1 Dec 1995 19:50:53 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Polishchuk",
"Alexander",
""
]
] | alg-geom | \section{Symplectic biextensions}
Let $X$ be an abelian variety.
A {\it biextension} of $X^2$ is a line bundle $L$ on $X^2$
together with isomorphisms
\begin{align*}
&L_{x+x',y}\simeq L_{x,y}\otimes L_{x',y},\\
&L_{x,y+y'}\simeq L_{x,y}\otimes L_{x,y'}
\end{align*}
--- this is a symbolic notation for isomorphisms
$(p_... |
1994-07-10T15:37:58 | 9407 | alg-geom/9407004 | en | https://arxiv.org/abs/alg-geom/9407004 | [
"alg-geom",
"math.AG"
] | alg-geom/9407004 | Andreas Steffens | Andreas Steffens | On the stability of the tangent bundle of Fano manifolds | 9 pages, LaTeX, to appear in Math. Ann | null | null | null | null | 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... | [
{
"version": "v1",
"created": "Sun, 10 Jul 1994 14:39:02 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Steffens",
"Andreas",
""
]
] | alg-geom | \section*{Introduction}
A smooth variety $X$ over the field of complex numbers ${\Bbb C}$ is called
{\em Fano} if its anticanonical divisor $-\!K_X$ is ample.
Stability (in the sense of Mumford and Takemoto)
with respect to $-K_X$ of the tangent bundle $T_X$ can be considered as an
algebraic analogue to the existence o... |
1994-07-18T17:00:32 | 9407 | alg-geom/9407010 | en | https://arxiv.org/abs/alg-geom/9407010 | [
"alg-geom",
"math.AG"
] | alg-geom/9407010 | Richard Hain | Richard Hain and Jun Yang | Real Grassmann Polylogarithms and Chern Classes | 42 pages, amslatex | null | null | null | null | 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-po... | [
{
"version": "v1",
"created": "Mon, 18 Jul 1994 15:00:10 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Hain",
"Richard",
""
],
[
"Yang",
"Jun",
""
]
] | alg-geom | \section{Introduction}\label{intro}
In this paper we define and prove the existence of real Grassmann
polylogarithms which are the real single-valued analogues of the
Grassmann polylogarithms defined in \cite{hain-macp} and constructed
in \cite{hain-macp,hana-macp,hana-macp_2,hain:generic}. We prove
that if $\eta_X$ i... |
1994-07-14T16:55:43 | 9407 | alg-geom/9407008 | en | https://arxiv.org/abs/alg-geom/9407008 | [
"alg-geom",
"math.AG"
] | alg-geom/9407008 | Clint McCrory | Gary Kennedy, Clint McCrory, and Shoji Yokura | Natural transformations from constructible functions to homology | 5 pages, AMSLaTeX, University of Georgia Math. Preprint Series | null | null | 20, Volume 2, 1994 | null | 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.)
| [
{
"version": "v1",
"created": "Thu, 14 Jul 1994 14:46:26 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Kennedy",
"Gary",
""
],
[
"McCrory",
"Clint",
""
],
[
"Yokura",
"Shoji",
""
]
] | alg-geom | \section{Introduction}
\label{intro}
\par
The MacPherson-Schwartz-Chern class natural
transformation $\mpc$ from the constructible functions
functor to homology \cite{macp} \cite{bs} satisfies
a remarkably stringent
normalization requirement:
for each nonsingular variety $X$, the element
$\mpc(\cf_X)$ of homology
assig... |
1995-03-07T06:20:08 | 9407 | alg-geom/9407012 | en | https://arxiv.org/abs/alg-geom/9407012 | [
"alg-geom",
"math.AG"
] | alg-geom/9407012 | Torres Fernando | Fernando Torres | On certain N--sheeted coverings and numerical semigroups which cannot be
realized as Weierstrass semigroups | ICTP preprint, 18 pages, Latex v. 2.1. Reason for resubmission: (1) I
reformulated the principal result (Theorem A) in order to obtain a better
bound on the genus for the results concerning semigroups. Remarks 3.11
contains examples that show the sharpness (or the necessity of the
hypothesis) of most of the res... | Com. Alg. 23(11) (1995) | null | null | null | 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... | [
{
"version": "v1",
"created": "Tue, 26 Jul 1994 17:58:41 GMT"
},
{
"version": "v2",
"created": "Mon, 29 Aug 1994 14:51:20 GMT"
},
{
"version": "v3",
"created": "Mon, 6 Mar 1995 15:07:39 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Torres",
"Fernando",
""
]
] | alg-geom | \section{Introduction.}
In Weierstrass Point Theory one associates a numerical semigroup to any
non--singular point $P$ of a
projective, irreducible, algebraic curve defined over an
algebraically closed field. This semigroup is called the
Weierstrass semigroup at $P$ and is the same for all but finitely many
points. T... |
1994-07-04T20:17:29 | 9407 | alg-geom/9407003 | en | https://arxiv.org/abs/alg-geom/9407003 | [
"alg-geom",
"math.AG"
] | alg-geom/9407003 | Raghu Nyshadham | I.Biswas and N.Raghavendra | Canonical Generators for the Cohomology of Moduli of Parabolic Bundles
on Curves | 22 pages, Latex Version 2.09 | null | null | null | null | 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 st... | [
{
"version": "v1",
"created": "Mon, 4 Jul 1994 18:04:51 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Biswas",
"I.",
""
],
[
"Raghavendra",
"N.",
""
]
] | alg-geom | \section{Introduction}
The aim of this paper is to determine generators of the
rational cohomology algebras of moduli spaces of parabolic
vector bundles on a curve, under some `primality' conditions
(see Assumptions 1.1 and 1.2)
on the parabolic datum. These generators are
canonical in a sense which will be made preci... |
1992-08-22T00:13:15 | 9208 | alg-geom/9208004 | en | https://arxiv.org/abs/alg-geom/9208004 | [
"alg-geom",
"math.AG"
] | alg-geom/9208004 | Rick Miranda | Rick Miranda | Torsion Sections of Semistable Elliptic Surfaces | 16 pages, AmsLatex 1.0 | null | null | null | null | Let S be a torsion section of an elliptic surface with only I_n fibers. This
article addresses the question: which components of singular fibers can S pass
through? We give necessary criteria for the "component numbers", and show an
equidistribution result for torsion sections of prime order.
| [
{
"version": "v1",
"created": "Fri, 21 Aug 1992 22:14:54 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Miranda",
"Rick",
""
]
] | alg-geom | \section{Introduction}
In this article we would like to address the following situation.
Let $f:X \to C$ be an elliptic surface with section $S_0$.
We further assume that $X$ is relatively minimal and smooth,
and that all singular fibers are semistable,
that is, are cycles of ${\Bbb P}^1$'s
(type ``$I_m$'' in Kodaira'... |
1992-10-10T15:49:11 | 9210 | alg-geom/9210003 | en | https://arxiv.org/abs/alg-geom/9210003 | [
"alg-geom",
"math.AG"
] | alg-geom/9210003 | Tyurin | Andrej Tyurin | The simple method of distinguishing the underlying differentiable
structures of algebraic surfaces | 24 pages, Latex | null | null | null | null | The simplest version of the Spin-polynomial invariants of the underlying
differentiable structures of algebraic surfaces were considered and the
simplest arguments were used in order to distinguish the underlying smooth
structures of certain algebraic surfaces.
| [
{
"version": "v1",
"created": "Sat, 10 Oct 1992 13:32:51 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Tyurin",
"Andrej",
""
]
] | alg-geom | \section{ Introduction}
The purpose of this preprint is to construct a new invariant of the smooth
structure of a simply connected 4-manifold M so called Spin-polynomials
\[ \gamma^{g,C}_1 (2,c_1,c_2) \in S^{d_1} H^2(M, {\mathchoice {\hbox{$\sf\textstyle Z\kern-0.4em Z$}) {~~~~~} (0.1) \]
and to show how to us... |
1992-10-19T20:32:40 | 9210 | alg-geom/9210007 | en | https://arxiv.org/abs/alg-geom/9210007 | [
"alg-geom",
"math.AG"
] | alg-geom/9210007 | Michael Thaddeus | Michael Thaddeus | Stable pairs, linear systems and the Verlinde formula | 40 pages, LaTeX | null | null | null | null | We study the moduli problem of pairs consisting of a rank 2 vector bundle and
a nonzero section over a fixed smooth curve. The stability condition involves a
parameter; as it varies, we show that the moduli space undergoes a sequence of
flips in the sense of Mori. As applications, we prove several results about
modul... | [
{
"version": "v1",
"created": "Mon, 19 Oct 1992 19:31:10 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Thaddeus",
"Michael",
""
]
] | alg-geom | \section{#1} \setcounter{equation}{0}}
\renewcommand{\theequation}{\thesection .\arabic{equation}}
\newcommand{\re}[1]{{\bf (\ref{#1})}}
\newenvironment{thm}{ \addvspace{20pt} \def5pt{2pt} \refstepcounter{equation}
\noindent {\bf (\theequation)} \begin{em}}{\end{em} \par
\addvspace{20pt} \def5pt{2pt} }
\newenvironmen... |
1997-04-02T03:10:13 | 9703 | alg-geom/9703023 | en | https://arxiv.org/abs/alg-geom/9703023 | [
"alg-geom",
"math.AG"
] | alg-geom/9703023 | null | Lev A. Borisov | On Betti numbers and Chern classes of varieties with trivial odd
cohomology groups | 5 pages, LaTeX. It turned out that most of the results of the paper
are already known. The appropriate reference is added | null | null | null | null | It was noticed in a very recent preprint of T. Eguchi, K. Hori, and Ch.-Sh.
Xiong (hep-th/9703086) that a curious identity between Betti numbers and Chern
classes holds for many examples of Fano varieties. The goal of this paper is to
prove that for varieties with trivial odd cohomology groups this identity is
equiva... | [
{
"version": "v1",
"created": "Wed, 19 Mar 1997 01:58:15 GMT"
},
{
"version": "v2",
"created": "Wed, 2 Apr 1997 01:10:00 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Borisov",
"Lev A.",
""
]
] | alg-geom | \section{Introduction}
\noindent
Let $X$ be a smooth complex projective variety of dimension $n$ whose odd cohomology
groups $H^{2k+1}({\bf C})$ are zero. It was noticed in \cite{tekhcx} that
a curious identity
$$\frac 14 \sum_k h^{2k} (k-\frac{n-1}2)(1-k+\frac{n-1}2)=
\frac1{24}\left(\frac{3-n}2\chi(X)-\int_Xc_1(X)... |
1997-04-16T05:26:52 | 9703 | alg-geom/9703011 | en | https://arxiv.org/abs/alg-geom/9703011 | [
"alg-geom",
"dg-ga",
"math.AG",
"math.DG"
] | alg-geom/9703011 | Philip A. Foth | Jean-Luc Brylinski and Philip Foth | Moduli of flat bundles on open Kaehler manifolds | LaTeX 21p, revised | null | null | null | null | We consider the moduli space MN of flat unitary connections on an open
Kaehler manifold U (complement of a divisor with normal crossings) with
restrictions on their monodromy transformations. Using intersection and L2
cohomologies with degenerating coefficients we construct a natural symplectic
form F on MN. When U i... | [
{
"version": "v1",
"created": "Sun, 9 Mar 1997 07:25:11 GMT"
},
{
"version": "v2",
"created": "Wed, 16 Apr 1997 03:26:48 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Brylinski",
"Jean-Luc",
""
],
[
"Foth",
"Philip",
""
]
] | alg-geom | \section{Introduction}
\setcounter{equation}{0}
Let $X$ be a compact K\"{a}hler manifold and $D$ a divisor on $X$ with normal
crossings. There exists a moduli space ${{\cal M}_{\cal N}}$ of flat irreducible unitary bundles
on $U=X\setminus D$ such that the monodromy transformation around each smooth
irreducible compon... |
1998-07-18T17:11:59 | 9703 | alg-geom/9703038 | en | https://arxiv.org/abs/alg-geom/9703038 | [
"alg-geom",
"math.AG"
] | alg-geom/9703038 | Vladimir Baranovsky | Vladimir Baranovsky | On Punctual Quot Schemes for Algebraic Surfaces | Latex2e, amssymb, amsmath packages; 4 pages. Proofs simplified | null | null | null | null | The punctual Quot scheme parametrizes all length d quotients of a (locally)
trivial rank r sheaf which are supported at a fixed point. The author shows
that this scheme is irreducible and (rd-1)-dimensional. The same result was
proved independently by Ellingsrud and Lehn.
| [
{
"version": "v1",
"created": "Fri, 28 Mar 1997 21:20:10 GMT"
},
{
"version": "v2",
"created": "Fri, 11 Apr 1997 23:41:28 GMT"
},
{
"version": "v3",
"created": "Sat, 18 Jul 1998 15:12:00 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Baranovsky",
"Vladimir",
""
]
] | alg-geom | \section*{Introduction.}
Let $S$ be a smooth projective surface over the field of complex
numbers $\mathbb{C}$. Fix a closed point $s \in S$ and a pair of positive
integers $r, d$. By results of Grothendieck (cf. \cite{G}, \cite{S})
there exists a projective scheme $\mathrm{Quot}_{[s]}(r, d)$ parametr... |
1997-07-21T20:16:21 | 9703 | alg-geom/9703002 | en | https://arxiv.org/abs/alg-geom/9703002 | [
"alg-geom",
"math.AG"
] | alg-geom/9703002 | Ludmil Katzarkov | Fedor Bogomolov and Ludmil Katzarkov | Complex projective surfaces and infinite groups | 29 pages, some comments and examples added LaTeX 2.09 | null | null | null | null | The paper contains a general construction which produces new examples of non
simply-connected smooth projective surfaces. We analyze the resulting surfaces
and their fundamental groups. Many of these fundamental groups are expected to
be non-residually finite. Using the construction we also suggest a series of
potent... | [
{
"version": "v1",
"created": "Mon, 3 Mar 1997 00:14:12 GMT"
},
{
"version": "v2",
"created": "Mon, 21 Jul 1997 18:12:57 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Bogomolov",
"Fedor",
""
],
[
"Katzarkov",
"Ludmil",
""
]
] | alg-geom | \section{Introduction}
It is well known that complex projective surfaces can have highly
nontrivial fundamental groups. It is also known that not all
finitely presented groups can occur as fundamental groups of
projective surfaces. The fundamental problem in the theory then, is to
determine which groups can occur a... |
1997-03-07T13:47:00 | 9703 | alg-geom/9703009 | en | https://arxiv.org/abs/alg-geom/9703009 | [
"alg-geom",
"math.AG"
] | alg-geom/9703009 | Klaus Hulek | C. Ciliberto, K. Hulek | A Remark on the Geometry of Elliptic Scrolls and Bielliptic Surfaces | LaTeX2e with theorem, amstex, amssymb, amscd packages; 11 pages | null | null | null | null | The union of two quintic elliptic scrolls in P^4 intersecting transversally
along an elliptic normal quintic curve is a singular surface Z which behaves
numerically like a bielliptic surface. In the appendix to the paper [W. Decker
et al.: Syzygies of abelian and bielliptic surfaces in P^4, alg-geom/9606013]
where th... | [
{
"version": "v1",
"created": "Fri, 7 Mar 1997 12:46:00 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Ciliberto",
"C.",
""
],
[
"Hulek",
"K.",
""
]
] | alg-geom | \section{Introduction}
The union of two quintic elliptic scrolls in ${\Bbb{P}}^4$
intersecting transversally along an elliptic normal quintic curve is a
singular surface $Z$ which behaves numerically like a bielliptic surface.
In the appendix to the paper \cite{ADHPR} where the equations of this
singular surface were c... |
1997-03-11T23:44:46 | 9703 | alg-geom/9703015 | en | https://arxiv.org/abs/alg-geom/9703015 | [
"alg-geom",
"math.AG"
] | alg-geom/9703015 | Andrew Kresch | Andrew Kresch | Associativity relations in quantum cohomology | LaTeX2e, 22 pages | null | null | null | null | We describe interdependencies among the quantum cohomology associativity
relations. We strengthen the first reconstruction theorem of Kontsevich and
Manin by identifying a subcollection of the associativity relations which
implies the full system of WDVV equations. This provides a tool for identifying
non-geometric s... | [
{
"version": "v1",
"created": "Tue, 11 Mar 1997 22:44:00 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Kresch",
"Andrew",
""
]
] | alg-geom | \section{Introduction}
\label{intro}
The geometry of moduli spaces of stable maps of genus 0
curves into a complex projective manifold $X$ leads to
a system of quadratic equations in the tree-level
(genus 0) {\em Gromov-Witten numbers} of $X$.
These quadratic equations were written down by physicists before the
geome... |
1997-03-05T05:01:20 | 9703 | alg-geom/9703004 | en | https://arxiv.org/abs/alg-geom/9703004 | [
"alg-geom",
"math.AG"
] | alg-geom/9703004 | Philip A. Foth | Philip A. Foth | Geometry of Moduli Spaces of Flat Bundles on Punctured Surfaces | LaTeX, 12 pages | null | null | null | null | We consider the moduli spaces of flat $SL(n, C)$-bundles on Riemann surfaces
with one puncture when we fix the conjugacy class ${\cal C}$ of the monodromy
transformation around the puncture. We show that under a certain condition on
the class ${\cal C}$ (namely the product of $k<n$ eigenvalues is not equal to
$1$) th... | [
{
"version": "v1",
"created": "Wed, 5 Mar 1997 04:01:15 GMT"
}
] | 2016-08-30T00:00:00 | [
[
"Foth",
"Philip A.",
""
]
] | alg-geom | \section{Introduction}
\setcounter{equation}{0}
Let $X$ be a Riemann surface of the genus $g>0$ with one puncture.
We consider the moduli space of flat $GL(n, {\Bbb C})$-bundles such that the
monodromy transformation around the puncture belongs to a given conjugacy class
${\cal C}\in SL(n, {\Bbb C})$. We further assum... |
1999-04-12T11:59:07 | 9703 | alg-geom/9703008 | en | https://arxiv.org/abs/alg-geom/9703008 | [
"alg-geom",
"math.AG"
] | alg-geom/9703008 | Angelo Vistoli | Angelo Vistoli | The deformation theory of local complete intersections | 52 pages. Plain TeX file, with AMS fonts and Eplain macro package
(included). Many typos have been corrected, and some material has been added | null | null | null | null | This is an expository paper on the subject of the title. It assumes basic
scheme theory, commutative and homological algebra.
| [
{
"version": "v1",
"created": "Thu, 6 Mar 1997 15:55:13 GMT"
},
{
"version": "v2",
"created": "Mon, 12 Apr 1999 09:59:06 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Vistoli",
"Angelo",
""
]
] | alg-geom | |
1997-03-22T17:23:09 | 9703 | alg-geom/9703030 | en | https://arxiv.org/abs/alg-geom/9703030 | [
"alg-geom",
"math.AG"
] | alg-geom/9703030 | Dan Cohen | Daniel C. Cohen, Alexander I. Suciu | Alexander Invariants of Complex Hyperplane Arrangements | 26 pages; LaTeX2e with amscd, amssymb packages | Trans. Amer. Math. Soc. 351 (1999), no. 10, 4043-4067 | 10.1090/S0002-9947-99-02206-0 | null | null | Let A be an arrangement of complex hyperplanes. The fundamental group of the
complement of A is determined by a braid monodromy homomorphism from a finitely
generated free group to the pure braid group. Using the Gassner representation
of the pure braid group, we find an explicit presentation for the Alexander
invari... | [
{
"version": "v1",
"created": "Sat, 22 Mar 1997 16:22:59 GMT"
}
] | 2010-10-26T00:00:00 | [
[
"Cohen",
"Daniel C.",
""
],
[
"Suciu",
"Alexander I.",
""
]
] | alg-geom | \section*{Introduction}\label{sec:intro}
Let ${\mathcal A} =\{H_{1},\dots ,H_{n}\}$ be an arrangement of hyperplanes in
${\mathbb C} ^{d}$, with complement $M={\mathbb C} ^{d} \setminus \cup_{i=1}^n H_{i}$,
and group $G=\pi _{1}(M)$. Let ${M'}$ be the maximal abelian cover,
corresponding to the abelianization $\ab... |
1997-02-28T17:48:10 | 9703 | alg-geom/9703001 | en | https://arxiv.org/abs/alg-geom/9703001 | [
"alg-geom",
"math.AG",
"math.CO"
] | alg-geom/9703001 | Frank Sottile | Nantel Bergeron and Frank Sottile | Schubert polynomials, the Bruhat order, and the geometry of flag
manifolds | Revised version of MSRI preprint \# 1996 - 083, 61 pages with 36
figures, where 15 of the pages and 26 of the figures are in an appendix
containing examples of the major geometric and combinatorial results LaTeX 2e | Duke Math. J., Vol 95 (1998) pp. 373-423 | 10.1215/S0012-7094-98-09511-4 | MSRI 1996-083 | null | We illuminate the relation between the Bruhat order on the symmetric group
and structure constants (Littlewood-Richardson coefficients) for the cohomology
of the flag manifold in terms of its basis of Schubert classes. Equivalently,
the structure constants for the ring of polynomials in variables $x_1,x_2,...$
in ter... | [
{
"version": "v1",
"created": "Fri, 28 Feb 1997 16:47:46 GMT"
}
] | 2016-11-08T00:00:00 | [
[
"Bergeron",
"Nantel",
""
],
[
"Sottile",
"Frank",
""
]
] | alg-geom | \section*{Introduction}
Extending work of Demazure~\cite{Demazure} and of Bernstein, Gelfand, and
Gelfand~\cite{BGG}, in 1982 Lascoux and
Sch\"utzenberger~\cite{Lascoux_Schutzenberger_polynomes_schubert}
defined remarkable polynomial representatives for Schubert classes in
the cohomology of a flag manifold, which they... |
1997-03-21T20:35:57 | 9703 | alg-geom/9703028 | en | https://arxiv.org/abs/alg-geom/9703028 | [
"alg-geom",
"math.AG"
] | alg-geom/9703028 | Jim Alexander | J. Alexander, A. Hirschowitz | Interpolation on Jets | 5 pages, Latex2e | null | null | null | null | We show that for any finite generic union of pairs $(x_i,L_i)_i$ where
$x_i\in L_i$ is a point of the line $L_i$ in projective $n$-space, the divisors
$m_ix_i$ on the $L_i$ have maximal rank with respect to homogeneous $d$ forms
for all $d\geq 0$ and all $m_i\geq 0$ modulo the expected numerical
restrictions.
| [
{
"version": "v1",
"created": "Fri, 21 Mar 1997 17:36:16 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Alexander",
"J.",
""
],
[
"Hirschowitz",
"A.",
""
]
] | alg-geom | \section{Introduction}
We work over a field $k$ of characteristic zero.
A {\em jet} in $n$-dimensional projective space
$\mbox{{\tenmsbm P}}_{k}^{\, n}$ over $k$
will be any divisor on a one dimensional linear
subspace (i.e. a line in $\mbox{{\tenmsbm P}}_{k}^{\,
n}$) with support a point. The {\em length} of a jet ... |
1998-07-13T11:39:31 | 9703 | alg-geom/9703013 | en | https://arxiv.org/abs/alg-geom/9703013 | [
"alg-geom",
"math.AG"
] | alg-geom/9703013 | Lars Ernstr{\o}m | Lars Ernstr\"om and Gary Kennedy | Contact Cohomology of the Projective Plane | 18 pages AMSLaTeX v 2e with xy-pic v 3.2; minor revison | null | null | null | null | We construct an associative ring which is a deformation of the quantum
cohomology ring of the projective plane. Just as the quantum cohomology encodes
the incidence characteristic numbers of rational plane curves, the contact
cohomology encodes the tangency characteristic numbers.
| [
{
"version": "v1",
"created": "Mon, 10 Mar 1997 11:36:58 GMT"
},
{
"version": "v2",
"created": "Mon, 9 Mar 1998 08:44:53 GMT"
},
{
"version": "v3",
"created": "Mon, 13 Jul 1998 09:39:32 GMT"
}
] | 2016-08-15T00:00:00 | [
[
"Ernström",
"Lars",
""
],
[
"Kennedy",
"Gary",
""
]
] | alg-geom | \section{Introduction}
\label{intro}
\par
In this paper we construct an associative ring which we call the {\em contact cohomology ring} of the projective plane. We believe that an analogous construction should work for all homogeneous varieties, but in our proof of associativity we rely on certain technical results fr... |
2000-02-15T17:21:37 | 9703 | alg-geom/9703037 | en | https://arxiv.org/abs/alg-geom/9703037 | [
"alg-geom",
"math.AG"
] | alg-geom/9703037 | Jim Alexander | J. Alexander, A. Hirschowitz | An Assympotic Vanishing Theorem for Generic Unions of Multiple Points | 26 pages, Latex 2e, using diagrams.tex. Revised edition | null | null | null | null | In this revised form, the proof of the principal lemma has been simplified
and the main theorem has been extended to all characteristics for those
varieties which are smooth in codimension one.
This principal theorem essentially says the following : given an ample line
bundle O(1) on a projective variety X and a fi... | [
{
"version": "v1",
"created": "Fri, 28 Mar 1997 16:19:40 GMT"
},
{
"version": "v2",
"created": "Fri, 2 May 1997 16:15:18 GMT"
},
{
"version": "v3",
"created": "Tue, 15 Feb 2000 16:21:36 GMT"
}
] | 2009-09-25T00:00:00 | [
[
"Alexander",
"J.",
""
],
[
"Hirschowitz",
"A.",
""
]
] | alg-geom | \section{Introduction}
This work is devoted to the following asymptotic statement :
\begin{thm}\label{thmm} Let $X$ be a projective geometrically reduced
and irreducible scheme over a field $k$ of (arbitrary) characteristic
$p$ and let $\fasm M\, ,\, \fasm L$ be line bundles on $X$ with $\fasm
L$ ample. If $p$ is pos... |
1997-06-07T01:37:14 | 9703 | alg-geom/9703021 | en | https://arxiv.org/abs/alg-geom/9703021 | [
"alg-geom",
"math.AG"
] | alg-geom/9703021 | Alexander Polishchuk | Alexander Polishchuk | Determinant bundles for abelian schemes | 26 pages, AMSLatex. One proof is shortened, a new linear relation
between determinant bundles is proven | null | null | null | null | To a symmetric, relatively ample line bundle on an abelian scheme one can
associate a linear combination of the determinant bundle and the relative
canonical bundle, which is a torsion element in the Picard group of the base.
We improve the bound on the order of this element found by Faltings and Chai.
In particular,... | [
{
"version": "v1",
"created": "Tue, 18 Mar 1997 21:14:24 GMT"
},
{
"version": "v2",
"created": "Fri, 6 Jun 1997 23:41:41 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Polishchuk",
"Alexander",
""
]
] | alg-geom | \section{The behavior under isogenies}
\label{behisog}
In this section we study the relation between $\Delta(L)$
and $\Delta(\a^*L)$ where $\a:A\rightarrow B$ is an isogeny of abelian schemes,
$L$ is a relatively ample, symmetric, line bundle on $B$
trivialized along the zero section. Let $d=\opera... |
1997-03-26T11:50:33 | 9703 | alg-geom/9703033 | en | https://arxiv.org/abs/alg-geom/9703033 | [
"alg-geom",
"math.AG"
] | alg-geom/9703033 | Wolfgang Eholzer | W. Eholzer, T. Ibukiyama | Rankin-Cohen Type Differential Operators for Siegel Modular Forms | 19 pages LaTeX2e using amssym.def | null | null | preprint MPI, DAMTP-97-26 | null | Let H_n be the Siegel upper half space and let F and G be automorphic forms
on H_n of weights k and l, respectively. We give explicit examples of
differential operators D acting on functions on H_n x H_n such that the
restriction of D(F(Z_1) G(Z_2)) to Z = Z_1 = Z_2 is again an automorphic form
of weight k+l+v on H_n... | [
{
"version": "v1",
"created": "Wed, 26 Mar 1997 10:50:10 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Eholzer",
"W.",
""
],
[
"Ibukiyama",
"T.",
""
]
] | alg-geom | \section{Introduction}
In this paper we are concerned with the explicit construction
of bilinear differential operators for Siegel modular forms mapping
$M(\Gamma)_k\times M(\Gamma)_l$ to $M(\Gamma)_{k+l+v}$
for all even non-negative integers $v$ and $\Gamma$
some discrete subgroup of $\mbox{{\rm{Sp}}}(2n,\R)$ with... |
1997-12-01T00:05:28 | 9703 | alg-geom/9703022 | en | https://arxiv.org/abs/alg-geom/9703022 | [
"alg-geom",
"math.AG"
] | alg-geom/9703022 | Edward Frenkel | E. Frenkel, D. Gaitsgory, D. Kazhdan, K. Vilonen | Geometric Realization of Whittaker Functions and the Langlands
Conjecture | 33 pages, LATEX2e | null | null | null | null | We prove the equivalence of two conjectural constructions of unramified
cuspidal automorphic functions on the adelic group GL_n(A) associated to an
irreducible l-adic local system of rank n on an algebraic curve X over a finite
field. The existence of such a function is predicted by the Langlands
conjecture.
The fi... | [
{
"version": "v1",
"created": "Tue, 18 Mar 1997 22:16:39 GMT"
},
{
"version": "v2",
"created": "Sun, 30 Nov 1997 23:05:28 GMT"
}
] | 2016-08-30T00:00:00 | [
[
"Frenkel",
"E.",
""
],
[
"Gaitsgory",
"D.",
""
],
[
"Kazhdan",
"D.",
""
],
[
"Vilonen",
"K.",
""
]
] | alg-geom | \section{Introduction}
\subsection{} Let $X$ be a smooth, complete, geometrically connected curve
over $\Fq$. Denote by $F$ the field of rational functions on $X$, by
${\mathbb A}$ the ring of adeles of $F$, and by $\on{Gal}(\ol{F}/F)$
the Galois group of $F$.
The present paper may be considered as a step towards und... |
1997-03-19T22:48:46 | 9703 | alg-geom/9703024 | en | https://arxiv.org/abs/alg-geom/9703024 | [
"alg-geom",
"math.AG"
] | alg-geom/9703024 | Ludwig Balke | Ludwig Balke | A note on P-resolutions of cyclic quotient singularities | 8 pages, 4 Postscript figures | null | null | null | null | P-resolutions of a cyclic quotient singularity are known to be in one-to-one
correspondence with the components of the base space of its semi-universal
deformation. Stevens and Christophersen have shown that P-resolutions are
parametrized by so-called chains representing zero or, equivalently, certain
subdivisions of... | [
{
"version": "v1",
"created": "Wed, 19 Mar 1997 21:48:29 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Balke",
"Ludwig",
""
]
] | alg-geom | \section{Introduction}
The discovery of Koll\'ar and Shepherd--Barron in
\cite{Kollar-Shepherd-Barron} that the reduced components of the
versal base space of a quotient singularity are in one-to-one
correspondence with the P-resolutions of this singularity provided a
more conceptual understanding of the deformation th... |
1997-03-09T13:15:39 | 9703 | alg-geom/9703012 | en | https://arxiv.org/abs/alg-geom/9703012 | [
"alg-geom",
"math.AG"
] | alg-geom/9703012 | Nitin Nitsure | Nitin Nitsure | Moduli of regular holonomic D-modules with normal crossing singularities | LaTeX, 41 pages, 124 KB | null | null | null | null | This paper solves the global moduli problem for regular holonomic D-modules
with normal crossing singularities on a nonsingular complex projective variety.
This is done by introducing a level structure (which gives rise to
``pre-D-modules''), and then introducing a notion of (semi-)stability and
applying Geometric In... | [
{
"version": "v1",
"created": "Sun, 9 Mar 1997 12:15:00 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Nitsure",
"Nitin",
""
]
] | alg-geom | \subsection*{\hbox{}\hfill{\normalsize\sl #1}\hfill\hbox{}}}
\textheight 23truecm \textwidth 15truecm
\addtolength{\oddsidemargin}{-1.05truecm}
\addtolength{\topmargin}{-1.5truecm}
\makeatletter \def\l@section{\@dottedtocline{1}{0em}{1.2em}} \makeatother
\begin{document}
\title{Moduli of regular holonomic ${\cal D}$-... |
1997-03-12T04:07:29 | 9703 | alg-geom/9703016 | en | https://arxiv.org/abs/alg-geom/9703016 | [
"alg-geom",
"math.AG"
] | alg-geom/9703016 | Misha S. Verbitsky | Misha Verbitsky | Hypercomplex Varieties | 40 pages LaTeX 2e | Comm. Anal. Geom. 7 (1999), no. 2, 355--396. | null | null | null | We give a number of equivalent definitions of hypercomplex varieties and
construct a twistor space for a hypercomplex variety. We prove that our
definition of a hypercomplex variety (used, e. g., in alg-geom/9612013) is
equivalent to a definition proposed by Deligne and Simpson, who used twistor
spaces. This gives a ... | [
{
"version": "v1",
"created": "Wed, 12 Mar 1997 03:07:14 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Verbitsky",
"Misha",
""
]
] | alg-geom | \section{Introduction}
Hypercomplex varieties are a very natural class of objects.
This notion allows one to speak uniformly of a number of
disparate examples coming from hyperk\"ahler geometry and the
theory of moduli spaces (\ref{_triana_hyperco_Remark_}, Subsection
\ref{_hyperholomo_Subsection_}).
A main prop... |
1997-03-21T13:39:06 | 9703 | alg-geom/9703026 | en | https://arxiv.org/abs/alg-geom/9703026 | [
"alg-geom",
"math.AG"
] | alg-geom/9703026 | Bill Oxbury | William Oxbury, Christian Pauly | Heisenberg invariant quartics and SU_C(2) for a curve of genus four | LaTeX, 36 pages, 2 figures | null | null | null | null | If C is a curve of genus 4 without vanishing theta-nulls then there exists a
unique (irreducible) Heisenberg-invariant quartic Q_C in |2\Theta| = P^{15}
such that Sing Q_C contains the image of SU_C(2), the moduli space of rank 2
vector bundles with trivial determinant. Moreover, in each eigen-P^7 of the
Heisenberg a... | [
{
"version": "v1",
"created": "Fri, 21 Mar 1997 12:38:27 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Oxbury",
"William",
""
],
[
"Pauly",
"Christian",
""
]
] | alg-geom | \section{\@startsection {section}{1}{{\bf Z}@}{-3.5ex plus -1ex minus
-.2ex}{1.5ex plus .2ex}{\large\bf}
\def\subsection{\@startsection{subsection}{2}{{\bf Z}@}{-3.25ex plus -1ex
minus
-.2ex}{1.5ex plus .2ex}{\normalsize\it}}
\let\emppsubsection\subsection
\newcommand{\numberequationsassubsubsections}
\newt... |
1997-03-24T19:22:55 | 9703 | alg-geom/9703031 | en | https://arxiv.org/abs/alg-geom/9703031 | [
"alg-geom",
"math.AG"
] | alg-geom/9703031 | Elizabeth Gasparim | Elizabeth Gasparim | On the topology of holomorphic bundles | null | null | null | null | null | In this work we study the topology of holomorphic rank two bundles over
complex surfaces. We consider bundles that are constructed by glueing and show
that under certain conditions the topology of the bundle does not depend on the
glueing. We present a simple classification of bundles on blown-up surfaces.
| [
{
"version": "v1",
"created": "Mon, 24 Mar 1997 19:02:29 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Gasparim",
"Elizabeth",
""
]
] | alg-geom | \section{Introduction}
Let $X$ be a complex manifold and let
$A$ and $B$ be open sets that cover $X.$
Given holomorphic bundles
$E_A$ and $E_B$ defined
over the subsets $A$ and $B,$ we construct
holomorphic bundles over $X$
by glueing the bundles $E_A$ and $E_B$ over $A \cap B.$
We then compare the topology o... |
1997-03-10T15:07:11 | 9703 | alg-geom/9703014 | en | https://arxiv.org/abs/alg-geom/9703014 | [
"alg-geom",
"math.AG"
] | alg-geom/9703014 | Gerd Mueller | Antonio Campillo, Janusz Grabowski, Gerd M\"uller | Derivation algebras of toric varieties | LaTeX, 14 pages | null | null | 1997/1, Mainz University | null | Normal affine algebraic varieties in characteristic 0 are uniquely determined
(up to isomorphism) by the Lie algebra of derivations of their coordinate ring.
This is not true without the hypothesis of normality. But, we show that (in
general, non-normal) toric varieties defined by simplicial affine semigroups
are uni... | [
{
"version": "v1",
"created": "Mon, 10 Mar 1997 14:07:12 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Campillo",
"Antonio",
""
],
[
"Grabowski",
"Janusz",
""
],
[
"Müller",
"Gerd",
""
]
] | alg-geom | \section{Introduction}
Normal affine algebraic varieties in characteristic 0
are uniquely determined (up to
isomorphism) by the Lie algebra of derivations of their coordinate
ring. This was shown by Siebert \cite{Si} and, independently, by Hauser
and the third author \cite{HM}. In both papers the assumption of
normalit... |
1995-06-05T06:20:29 | 9506 | alg-geom/9506007 | en | https://arxiv.org/abs/alg-geom/9506007 | [
"alg-geom",
"math.AG"
] | alg-geom/9506007 | Lisa Jeffrey | Lisa C. Jeffrey, Frances C. Kirwan | On localization and Riemann-Roch numbers for symplectic quotients | 19 pages; September 1994, revised March 1995, LaTeX v. 2.09 | Quart. J. Math. 47 (1996) 165-185 | null | null | null | Suppose $(M,\omega)$ is a compact symplectic manifold acted on by a compact
Lie group $K$ in a Hamiltonian fashion, with moment map $\mu: M \to \Lie(K)^*$
and Marsden-Weinstein reduction $M_{red} = \mu^{-1}(0)/K$. In this paper, we
assume that $M$ has a $K$-invariant K\"ahler structure. In an earlier paper, we
proved... | [
{
"version": "v1",
"created": "Sun, 4 Jun 1995 15:02:13 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Jeffrey",
"Lisa C.",
""
],
[
"Kirwan",
"Frances C.",
""
]
] | alg-geom | \section{Introduction}
Let $M$ be a compact symplectic manifold of (real) dimension $2m$,
acted on in a Hamiltonian fashion by a compact connected
Lie group $K$
with maximal torus $T$, and let $\liek$ and $\liet$ denote the
Lie algebras of $K$ and $T$. Let $\mu: M \to \lieks$
be a moment map for this action. The... |
1995-10-26T05:20:25 | 9506 | alg-geom/9506023 | en | https://arxiv.org/abs/alg-geom/9506023 | [
"alg-geom",
"math.AG"
] | alg-geom/9506023 | Kai Behrend | K. Behrend and Yu. Manin | Stacks of Stable Maps and Gromov-Witten Invariants | Postscript file available at
http://www.math.ubc.ca/people/faculty/behrend/gwi.ps , AMSLaTeX | null | null | null | null | We correct some errors in the earlier version of this paper. Most
importantly, the definition of isogeny of marked stable graphs has changed.
| [
{
"version": "v1",
"created": "Tue, 27 Jun 1995 14:32:00 GMT"
},
{
"version": "v2",
"created": "Thu, 26 Oct 1995 02:30:52 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Behrend",
"K.",
""
],
[
"Manin",
"Yu.",
""
]
] | alg-geom | \section{Introduction}
Let $V$ be a projective algebraic manifold. In \cite{KM}, Sec.\ 2,
Gromov-Witten invariants of $V$ were described
axiomatically as a collection of linear maps
\[I^{V}_{g,n,\beta}:\ H^{\ast}(V)^{\otimes n}\longrightarrow
H^{\ast}(\overline{M}_{g,n},{\Bbb Q}),\quad \beta\in H_2(V,{\Bbb Z})\]
satis... |
1996-03-31T05:48:29 | 9506 | alg-geom/9506012 | en | https://arxiv.org/abs/alg-geom/9506012 | [
"alg-geom",
"math.AG"
] | alg-geom/9506012 | Dmitri Orlov | A.Bondal and D.Orlov | Semiorthogonal decomposition for algebraic varieties | LaTeX 2.9 | null | null | null | null | A criterion for a functor between derived categories of coherent sheaves to
be full and faithful is given. A semiorthogonal decomposition for the derived
category of coherent sheaves on the intersection of two even dimensional
quadrics is obtained. The behaviour of derived categories with respect to
birational transf... | [
{
"version": "v1",
"created": "Mon, 19 Jun 1995 23:54:17 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Bondal",
"A.",
""
],
[
"Orlov",
"D.",
""
]
] | alg-geom | \section*{ SEMIORTHOGONAL DECOMPOSITIONS FOR ALGEBRAIC VARIETIES}
\begin{abstract}
A criterion for a functor between derived categories of coherent sheaves to be full and faithful is given. A semiorthogonal decomposition for the derived category of coherent sheaves on the intersection of two even dimensional quadrics i... |
1995-07-17T06:20:17 | 9506 | alg-geom/9506019 | en | https://arxiv.org/abs/alg-geom/9506019 | [
"alg-geom",
"math.AG"
] | alg-geom/9506019 | Lothar Goettsche | Geir Ellingsrud and Lothar G\"ottsche | Wall-crossing formulas, Bott residue formula and the Donaldson
invariants of rational surfaces | We correct some missing attributions and citations. In particular
this applies to the cited paper of Kotschick and Lisca "Instanton invariants
via topology", which contains some ideas which have been important for this
work. AMSLaTeX | null | null | null | null | We study the Donaldson invariants of rational surfaces and their dependence
on the chambers in the ample cone. We build on a previous joint paper in which
we have expressed the change of the Donaldson invariants on an algebraic
surface $S$ under crossing a so-called good wall in terms of certain
intersection numbers ... | [
{
"version": "v1",
"created": "Fri, 23 Jun 1995 14:16:50 GMT"
},
{
"version": "v2",
"created": "Sat, 15 Jul 1995 12:32:40 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Ellingsrud",
"Geir",
""
],
[
"Göttsche",
"Lothar",
""
]
] | alg-geom | P(n){P(n)}
\def{\text{\rom{\bf b}}}{{\text{\rom{\bf b}}}}
\defS^{(\bb)}{S^{({\text{\rom{\bf b}}})}}
\def{\text{\rom{\bf E}}}{{\text{\rom{\bf E}}}}
\def\Inc#1{Z_{#1}}
\def\inc#1{\zeta_{#1}}
\def\boh#1{pt_{#1}
\def\Boh#1{Pt_{#1}}
\def\mah#1{al_{#1}
\def\Mah#1{Al_{#1}}
\def\pr#1{W_{#1}}
\def\alpha{\alpha}
\def\Gamma{... |
1995-06-19T06:20:13 | 9506 | alg-geom/9506004 | en | https://arxiv.org/abs/alg-geom/9506004 | [
"alg-geom",
"hep-th",
"math.AG"
] | alg-geom/9506004 | Steven Duplij | Steven Duplij | On Alternative Supermatrix Reduction | 22 pages, Standard LaTeX with AmS fonts | Lett.Math.Phys. 37 (1996) 385 | 10.1007/BF00312670 | KL-TH-95/15 | null | We consider a nonstandard odd reduction of supermatrices (as compared with
the standard even one) which arises in connection with possible extension of
manifold structure group reductions. The study was initiated by consideration
of the generalized noninvertible superconformal-like transformations. The
features of ev... | [
{
"version": "v1",
"created": "Fri, 2 Jun 1995 14:33:30 GMT"
},
{
"version": "v2",
"created": "Fri, 16 Jun 1995 13:03:19 GMT"
}
] | 2009-10-28T00:00:00 | [
[
"Duplij",
"Steven",
""
]
] | alg-geom | \section{Introduction}
According to the general theory of $G$-structures \cite{che1,gui,kobayashi}
various
geometries are obtained by a reduction of a structure group of a manifold to
some subgroup $G$ of the tangent space endomorphisms. In the local approach
using coordinate description this means that one should re... |
1996-03-01T16:58:33 | 9506 | alg-geom/9506021 | en | https://arxiv.org/abs/alg-geom/9506021 | [
"alg-geom",
"math.AG"
] | alg-geom/9506021 | Herbert Lange | H. Lange | A Vector Bundle of Rank 2 on P1 x P3 | 20 pages, LaTeX | null | null | null | null | The paper studies a rank 2 vector bundle on P1 x P3. Similarly to the
Horrocks - Mumford bundle on P4 this vector bundle encodes a lot of geometric
information. It is defined via the Serre construction by an abelian surface in
P1 x P3. The bundle is stable with respect to O(1,1), its jumping lines are
determined. Mor... | [
{
"version": "v1",
"created": "Mon, 26 Jun 1995 13:12:44 GMT"
}
] | 2015-06-30T00:00:00 | [
[
"Lange",
"H.",
""
]
] | alg-geom | \section{Abelian surfaces in ${\bf P_1 \times P_3}$}
It is shown in [L]
that there is a two--parameter family of abelian surfaces
admitting an embedding into $\Bbb{P}_1 \times \Bbb{P}_3$. Moreover, it is proven that every
abelian surface in $\Bbb{P}_1 \times \Bbb{P}_3$ is a member of this family. Suppose $\varphi =... |
1995-11-18T22:12:09 | 9506 | alg-geom/9506010 | fr | https://arxiv.org/abs/alg-geom/9506010 | [
"alg-geom",
"math.AC",
"math.AG"
] | alg-geom/9506010 | Francois Lauze | Francois Lauze | Rang maximal pour $T_P^n$ | LateX 2e, in french, no more accents, major revision | null | null | null | null | In this paper, I compute the last non-trivial term of the minimal free
resolution of the homogeneous ideal of $s$ points of $P^n$ in sufficiently
general position, for any $s$, showing that this term is the one conjectured by
the Minimal Resolution Conjecture of Anna Lorenzini. I use a geometrical
method, the "vector... | [
{
"version": "v1",
"created": "Mon, 12 Jun 1995 16:00:10 GMT"
},
{
"version": "v2",
"created": "Tue, 13 Jun 1995 09:18:14 GMT"
},
{
"version": "v3",
"created": "Tue, 20 Jun 1995 09:44:16 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Lauze",
"Francois",
""
]
] | alg-geom | \subsection*{
\begin{center}
\thepara.~#1
\end{center}
}
}
\title{Rang maximal pour $\tp{n}$}
\author{Fran{\c{c}}ois Lauze \\
U.N.S.A Laboratoire de Math{\'e}matiques J. Dieudonn{\'e},
U.R.A 168\\
Parc Valrose, 06108 Nice Cedex 2\\
e-mail : lauze@math.unice.fr
}
... |
1995-07-17T06:20:11 | 9506 | alg-geom/9506018 | en | https://arxiv.org/abs/alg-geom/9506018 | [
"alg-geom",
"math.AG"
] | alg-geom/9506018 | Lothar Goettsche | Lothar G\"ottsche | Modular forms and Donaldson invariants for 4-manifolds with $b_+=1$ | I correct a number of missing attributions and citations. In
particular this applies to the cited paper of Kotschick and Lisca "Instanton
invariants via topology", which contains some ideas which have been important
for this work. AMSLaTeX | null | null | null | null | We study the Donaldson invariants of simply connected $4$-manifolds with
$b_+=1$, and in particular the change of the invariants under wall-crossing. We
assume the conjecture of Kotschick and Morgan about the shape of the
wall-crossing terms (which Oszva\'th and Morgan are now able to prove), and are
determine a gene... | [
{
"version": "v1",
"created": "Fri, 23 Jun 1995 12:26:25 GMT"
},
{
"version": "v2",
"created": "Sat, 15 Jul 1995 12:21:16 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Göttsche",
"Lothar",
""
]
] | alg-geom | P(n){P(n)}
\def{\text{\rom{\bf b}}}{{\text{\rom{\bf b}}}}
\defS^{(\bb)}{S^{({\text{\rom{\bf b}}})}}
\def{\text{\rom{\bf E}}}{{\text{\rom{\bf E}}}}
\def\Inc#1{Z_{#1}}
\def\inc#1{\zeta_{#1}}
\def\boh#1{pt_{#1}
\def\Boh#1{Pt_{#1}}
\def\mah#1{al_{#1}
\def\Mah#1{Al_{#1}}
\def\pr#1{W_{#1}}
\def\alpha{\alpha}
\def\Gamma{... |
1995-06-26T06:20:32 | 9506 | alg-geom/9506020 | en | https://arxiv.org/abs/alg-geom/9506020 | [
"alg-geom",
"hep-th",
"math.AG"
] | alg-geom/9506020 | Ian Grojnowski | I. Grojnowski (Yale) | Instantons and affine algebras I: The Hilbert scheme and vertex
operators | 14 pages, AmsTex | null | null | null | null | This is the first in a series of papers which describe the action of an
affine Lie algebra with central charge $n$ on the moduli space of
$U(n)$-instantons on a four manifold $X$. This generalises work of Nakajima,
who considered the case when $X$ is an ALE space. In particular, this describes
the combinatorial compl... | [
{
"version": "v1",
"created": "Sun, 25 Jun 1995 22:19:04 GMT"
}
] | 2015-06-30T00:00:00 | [
[
"Grojnowski",
"I.",
"",
"Yale"
]
] | alg-geom | \part{\Cal P}
\define\ce{\Cal E}
\define\ts{\widetilde{\Sigma}}
\define\hilb#1{\widetilde{S^{#1}X}}
\define\hilbs#1#2{\widetilde{S^{#1}_{#2}X}}
\define\tv#1{\Cal T_{\cv,{#1}}}
\define\quot{\frak Q \frak u \frak o \frak t}
\define\qbinom#1#2{\thickfracwithdelims[]\thickness0#1#2}
\head
Introduction
\endhead
This is... |
1995-06-16T06:20:15 | 9506 | alg-geom/9506011 | en | https://arxiv.org/abs/alg-geom/9506011 | [
"alg-geom",
"math.AG"
] | alg-geom/9506011 | Dr. P. E. Newstead | V. Balaji, L. Brambila Paz, and P. E. Newstead | Stability of the Poincar\'e bundle | 16pp. Hard copy available from Dr. P. E. Newstead, Dept. of Pure
Maths., University of Liverpool, Liverpool, L69 3BX, England. LaTeX 2.09 | null | null | null | null | Let $C$ be a nonsingular projective curve of genus $g\ge2$ defined over the
complex numbers, and let $M_{\xi}$ denote the moduli space of stable bundles of
rank $n$ and determinant $\xi$ on $C$, where $\xi$ is a line bundle of degree
$d$ on $C$ and $n$ and $d$ are coprime. It is shown that the universal bundle
$\cu_{... | [
{
"version": "v1",
"created": "Thu, 15 Jun 1995 14:20:53 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Balaji",
"V.",
""
],
[
"Paz",
"L. Brambila",
""
],
[
"Newstead",
"P. E.",
""
]
] | alg-geom | \section*{Introduction}
In the study of moduli spaces of stable bundles on an
algebraic curve $C$, various bundles on the moduli space or
on the product of the moduli space with $C$ arise in a
natural way. An interesting question to ask about any such
bundle is whether it is itself stable in some sense.
More precise... |
1997-09-16T23:10:42 | 9506 | alg-geom/9506002 | en | https://arxiv.org/abs/alg-geom/9506002 | [
"alg-geom",
"math.AG"
] | alg-geom/9506002 | Alan Durfee | Alan H. Durfee | The index of $grad f(x,y)$ | A thoroughly revised and hopefully more readable version; the main
results are the same. 35 pages with 7 figures | null | null | null | null | Let $f(x,y)$ be a real polynomial of degree $d$ with isolated critical
points, and let $i$ be the index of $grad f$ around a large circle containing
the critical points. An elementary argument shows that $|i| \leq d-1$. In this
paper we show that $ i \leq max \{1, d-3 \}$. We also show that if all the
level sets of $... | [
{
"version": "v1",
"created": "Thu, 1 Jun 1995 15:52:56 GMT"
},
{
"version": "v2",
"created": "Tue, 16 Sep 1997 21:05:48 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Durfee",
"Alan H.",
""
]
] | alg-geom | \section{#1}}
\newcounter{mycounter}[section]
\renewcommand{\themycounter}{\arabic{section}.\arabic{mycounter}}
\newenvironment{theorem}%
{\medskip
\refstepcounter{mycounter}
{\bf \noindent Theorem \themycounter.}\begin{em}}%
{\end{em} \medskip }
\newenvironment{proposition}%
{\medskip
\refstepcounter{... |
1996-02-27T06:25:20 | 9307 | alg-geom/9307002 | en | https://arxiv.org/abs/alg-geom/9307002 | [
"alg-geom",
"math.AG"
] | alg-geom/9307002 | Robert Friedman | Robert Friedman | Vector bundles and $SO(3)$ invariants for elliptic surfaces I | 19 pages, AMS-TeX | null | null | null | null | This paper is the first in a series of three devoted to the smooth
classification of simply connected elliptic surfaces. The method is to compute
some coefficients of Donaldson polynomials of $SO(3)$ invariants whose second
Stiefel-Whitney class is transverse to the unique primitive class $\kappa$ such
that a positiv... | [
{
"version": "v1",
"created": "Wed, 14 Jul 1993 16:07:28 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Friedman",
"Robert",
""
]
] | alg-geom | \section{1. Introduction.}
Beginning with Donaldson's seminal paper on the failure of the $h$-cobordism
theorem in dimension 4 [4], the techniques of gauge theory have proved to be
highly successful in analyzing the smooth structure of simply connected
elliptic
surfaces. Recall that a simply connected elliptic surface... |
1996-02-27T06:25:20 | 9307 | alg-geom/9307003 | en | https://arxiv.org/abs/alg-geom/9307003 | [
"alg-geom",
"math.AG"
] | alg-geom/9307003 | Robert Friedman | Robert Friedman | Vector bundles and $SO(3)$ invariants for elliptic surfaces II: The case
of even fiber degree | 18 pages, AMS-TeX | null | null | null | null | This paper is the second in a series of three devoted to the smooth
classification of simply connected elliptic surfaces. In this paper, we study
the case where one of the multiple fibers has even multiplicity, and describe
the moduli space of stable rank two vector bundles with the appropriate first
Chern class need... | [
{
"version": "v1",
"created": "Wed, 14 Jul 1993 16:08:53 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Friedman",
"Robert",
""
]
] | alg-geom | \section{Introduction.}
Let $S$ be a simply connected elliptic surface with at most two multiple
fibers.
In this paper, the second in a series of three, we are concerned with
describing
moduli spaces of stable vector bundles $V$ over $S$ such that the restriction
of $c_1(V)$ to a general fiber has the smallest possibl... |
1994-02-13T03:29:35 | 9307 | alg-geom/9307001 | en | https://arxiv.org/abs/alg-geom/9307001 | [
"alg-geom",
"math.AG"
] | alg-geom/9307001 | Lisa Jeffrey | L.C. Jeffrey and F.C. Kirwan | Localization for nonabelian group actions | 42 pages, LaTex version no. 2.09, Introduction and Section 8 have
been rewritten in revised version | null | null | null | null | Suppose $X$ is a compact symplectic manifold acted on by a compact Lie group
$K$ (which may be nonabelian) in a Hamiltonian fashion, with moment map $\mu: X
\to {\rm Lie}(K)^*$ and Marsden-Weinstein reduction $\xred = \mu^{-1}(0)/K$.
There is then a natural surjective map $\kappa_0$ from the equivariant
cohomology $H... | [
{
"version": "v1",
"created": "Tue, 6 Jul 1993 22:55:00 GMT"
},
{
"version": "v2",
"created": "Thu, 2 Sep 1993 22:01:00 GMT"
},
{
"version": "v3",
"created": "Sun, 13 Feb 1994 02:28:00 GMT"
}
] | 2008-02-03T00:00:00 | [
[
"Jeffrey",
"L. C.",
""
],
[
"Kirwan",
"F. C.",
""
]
] | alg-geom | \section{Introduction}
Suppose $X$ is a compact oriented manifold acted on by a compact
connected Lie group $K$ of dimension $s$; one may
then define the equivariant
cohomology $\hk(X)$.
Throughout this paper we shall consider only cohomology
with complex coefficients.
If $X$ is a symplectic manifold
with symplectic f... |
1993-07-30T20:12:40 | 9307 | alg-geom/9307010 | en | https://arxiv.org/abs/alg-geom/9307010 | [
"alg-geom",
"math.AG"
] | alg-geom/9307010 | Victor Batyrev | Victor V. Batyrev and Duco van Straten | Generalized Hypergeometric Functions and Rational Curves on Calabi-Yau
Complete Intersections in Toric Varieties | 45 pages, Latex 2.09 | Commun. Math. Phys. 168 (1995) 493 | 10.1007/BF02101841 | null | null | We formulate general conjectures about the relationship between the A-model
connection on the cohomology of a $d$-dimensional Calabi-Yau complete
intersection $V$ of $r$ hypersurfaces $V_1, \ldots, V_r$ in a toric variety
${\bf P}_{\Sigma}$ and the system of differential operators annihilating the
special hypergeomet... | [
{
"version": "v1",
"created": "Fri, 30 Jul 1993 18:43:36 GMT"
}
] | 2009-10-22T00:00:00 | [
[
"Batyrev",
"Victor V.",
""
],
[
"van Straten",
"Duco",
""
]
] | alg-geom | \section{Introduction}
\noindent
In this paper we consider complex projective smooth algebraic varieties
$V$ of dimension $d$ whose canonical bundles ${\cal K}_V$ are trivial,
i.e. ${\cal K}_V \cong {\cal O}_V$, and the Hodge numbers $h^{p,0}(V)$ are
zero unless $p=0$, or $p=d$. These varieties are called
{\em $d$-d... |
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