Gromov-Witten classes, quantum cohomology, and enumerative geometry

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. Applications to counting rational curves on del Pezzo surfaces and projective spaces are given.

field theory: topological
geometry: algebra
differential forms: symplectic
cohomology

References(4)

Figures(0)

- Duke Math.J. 4 63

Integrable systems in topological field theory

B. Dubrovin
(
- INFN, Naples
)

- Nucl.Phys.B 379 (1992) 627-689
•
DOI:
- 10.1016/0550-3213(92)90137-Z

- Trans.Am.Math.Soc. 330 545

Two-dimensional gravity and intersection theory on moduli space

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- Surveys Diff.Geom. 1 (1991) 243-310,
- In *Brezin, E. (ed.), Wadia, S.R. (ed.): The large N expansion in quantum field theory and statistical physics* 871-938. and In *Cambridge 1990, Proceedings, Surveys in differential geometry* 243-310
•
DOI:
- 10.4310/SDG.1990.v1.n1.a5