**Contemporary Mathematics**

Volume: 276;
2001;
294 pp;
Softcover

MSC: Primary 13; 14; 32; 53;
Secondary 20; 57; 65; 93

Print ISBN: 978-0-8218-2810-6

Product Code: CONM/276

List Price: $92.00

Individual Member Price: $73.60

**Electronic ISBN: 978-0-8218-7866-8
Product Code: CONM/276.E**

List Price: $92.00

Individual Member Price: $73.60

# Advances in Algebraic Geometry Motivated by Physics

Share this page *Edited by *
*Emma Previato*

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.

#### Readership

Graduate students and research mathematicians interested in algebraic geometry and related disciplines.

# Table of Contents

## Advances in Algebraic Geometry Motivated by Physics

- Contents vii8 free
- Introduction ix10 free
- Chapter I. Enumerative or reality problems 114 free
- Number of automorphisms of principally polarized abelian varieties 316
- Rational curves on Grassmannians: Systems theory, reality, and transversality 922
- Fundamental groups of line arrangements: Enumerative aspects 4356
- 1. Introduction 4457
- 2. Fundamental groups and Alexander matrices 4760
- 3. Resonance varieties and characteristic varieties 5164
- 4. Homology of finite-index subgroups and torsion points on varieties 5467
- 5. Congruence covers and polynomial periodicity 5568
- 6. Hirzebruch covering surfaces 5770
- 7. Counting finite-index subgroups 5972
- 8. Lower central series quotients and Chen groups 6174
- 9. Guide to examples 6578
- 10. Examples 6780
- References 7689

- Chapter II. Variational and moduli problems 8194
- The formula 12 = 10 + 2 x 1 and its generalizations: Counting rational curves on F2 8396
- Stable maps and Hurwitz schemes in mixed characteristics 89102
- On modular properties of odd theta-characteristics 101114
- Asymptotic Hodge theory and quantum products 115128
- On rational curves in n-space with given normal bundle 137150
- A tool for stable reduction of curves on surfaces 145158

- Chapter III. Mirror symmetry and Gromov-Witten invariants 155168
- Virtual fundamental classes of zero loci 157170
- Gravitational descendants and the moduli space of higher spin curves 167180
- Homological mirror symmetry in dimension one 179192
- The Hodge structure of semiample hypersurfaces and a generalization of the monomial-divisor mirror map 199212
- 1. A brief review of semiample divisors in toric varieties. 201214
- 2. The Hodge structure of semiample nondegenerate hypersurfaces. 204217
- 3. The Picard group of semiample hypersurfaces. 219232
- 4. The B-model correlation functions. 222235
- 5. A generalization of the monomial-divisor mirror map. 223236
- References 227240

- Algebraic construction of Witten's top Chern class 229242
- Symmetries of Gromov-Witten invariants 251264
- Gauge theory techniques in quantum cohomology 259272
- Gromov-Witten invariants of flag manifolds and products of conjugacy classes 279292

- Appendix 287300