Advances in Algebraic Geometry Motivated by Physics

Advances in Algebraic Geometry Motivated by Physics

by Emma Previato
     
 

ISBN-10: 082182810X

ISBN-13: 9780821828106

Pub. Date: 06/13/2001

Publisher: American Mathematical Society

Our knowledge of objects of algebraic geometry such as moduli of curves, (real) Schubert classes, fundamental groups of complements of hyperplane arrangements, toric varieties, and variation of Hodge structures, has been enhanced recently by ideas and constructions of quantum field theory, such as mirror symmetry, Gromov-Witten invariants, quantum cohomology, and

Overview

Our knowledge of objects of algebraic geometry such as moduli of curves, (real) Schubert classes, fundamental groups of complements of hyperplane arrangements, toric varieties, and variation of Hodge structures, has been enhanced recently by ideas and constructions of quantum field theory, such as mirror symmetry, Gromov-Witten invariants, quantum cohomology, and gravitational descendants. These are some of the themes of this refereed collection of papers, which grew out of the special session, ''Enumerative Geometry in Physics,'' held at the AMS meeting in Lowell, MA, April 2000. This session brought together mathematicians and physicists who reported on the latest results and open questions; all the abstracts are included as an Appendix, and also included are papers by some who could not attend. The collection provides an overview of state-of-the-art tools, links that connect classical and modern problems, and the latest knowledge available.

Product Details

ISBN-13:
9780821828106
Publisher:
American Mathematical Society
Publication date:
06/13/2001
Series:
Contemporary Mathematics Series, #276
Pages:
294
Product dimensions:
7.09(w) x 10.24(h) x (d)

Table of Contents

Introductionix
Chapter I.Enumerative or reality problems
Number of automorphisms of principally polarized abelian varieties3
Rational curves on Grassmannians: Systems theory, reality, and transversality9
Fundamental groups of line arrangements: Enumerative aspects43
Chapter II.Variational and moduli problems
The formula 12 = 10 + 2 [times] 1 and its generalizations: Counting rational curves on F[subscript 2]83
Stable maps and Hurwitz schemes in mixed characteristics89
On modular properties of odd theta-characteristics101
Asymptotic Hodge theory and quantum products115
On rational curves in n-space with given normal bundle137
A tool for stable reduction of curves on surfaces145
Chapter III.Mirror symmetry and Gromov-Witten invariants
Virtual fundamental classes of zero loci157
Gravitational descendants and the moduli space of higher spin curves167
Homological mirror symmetry in dimension one179
The Hodge structure of semiample hypersurfaces and a generalization of the monomial-divisor mirror map199
Algebraic construction of Witten's top Chern class229
Symmetries of Gromov-Witten invariants251
Gauge theory techniques in quantum cohomology259
Gromov-Witten invariants of flag manifolds and products of conjugacy classes279
Appendix
AppendixThe Lowell meeting289

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