Advances in Algebraic Geometry Motivated by Physics

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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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.

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Editorial Reviews

Booknews
Featuring the recent work of mathematicians and physicists, the proceedings from this April 2000 conference in Lowell, Massachusetts, include 17 papers on enumerative or reality problems, variational and moduli problems, and mirror symmetry and Gromov-Witten invariants. More specifically, the papers deal with topics like Schubert classes, hyperplane arrangements, quantum field theory, and gravitational descendants. All the abstracts from the conference are included in the appendix. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Table of Contents

Introduction
Number of automorphisms of principally polarized abelian varieties 3
Rational curves on Grassmannians: Systems theory, reality, and transversality 9
Fundamental groups of line arrangements: Enumerative aspects 43
The formula 12 = 10 + 2 x 1 and its generalizations: Counting rational curves on F[subscript 2] 83
Stable maps and Hurwitz schemes in mixed characteristics 89
On modular properties of old theta-characteristics 101
Asymptotic Hodge theory and quantum products 115
On rational curves in n-space with given normal bundle 137
A tool for stable reduction of curves on surfaces 145
Virtual fundamental classes of zero loci 157
Gravitational descendants and the moduli space of higher spin curves 167
Homological mirror symmetry in dimension one 179
The Hodge structure of semiample hypersurfaces and a generalization of the monomial-divisor mirror map 199
Algebraic construction of Witten's top Chern class 229
Symmetries of Gromov-Witten invariants 251
Gauge theory techniques in quantum cohomology 259
Gromov-Witten invariants of flag manifolds and products of conjugacy classes 279
App The Lowell meeting 289
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