DMCA
Gromov-Witten classes, quantum cohomology, and enumerative geometry (1994)
| Venue: | Commun. Math. Phys |
| Citations: | 475 - 3 self |
BibTeX
@ARTICLE{Kontsevich94gromov-wittenclasses,,
author = {M. Kontsevich and Yu. Manin},
title = {Gromov-Witten classes, quantum cohomology, and enumerative geometry},
journal = {Commun. Math. Phys},
year = {1994},
pages = {525}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological Field Theories are defined, and it is proved that tree level theories are determined by their correlation functions. Application to counting rational curves on del Pezzo surfaces and projective spaces are given. Let V be a projective algebraic manifold. Methods of quantum field theory recently led to a prediction of some numerical characteristics of the space of algebraic curves in V, especially of genus zero, eventually endowed with a parametrization and marked points. It turned out that
Keyphrases
enumerative geometry quantum cohomology gromov-witten class projective algebraic manifold cohomological field theory gromov witten numerical characteristic tree level theory algebraic geometry correlation function topological quantum field theory quantum field theory mathematical aspect axiomatic treatment algebraic curve del pezzo surface fano variety genus zero projective space rational curve
