Gromov-Witten invariants on Grassmannians

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We prove that any three-point genus zero Gromov-Witten invariant on a type A Grassmannian is equal to a classical intersection number on a two-step flag variety. We also give symplectic and orthogonal analogues of this result; in these cases the two-step flag variety is replaced by a sub-maximal isotropic Grassmannian. Our theorems are applied, in type A, to formulate a conjectural quantum Littlewood-Richardson rule, and in the other classical Lie types, to obtain new proofs of the main structure theorems for the quantum cohomology of Lagrangian and orthogonal Grassmannians.
15 pages, LaTeX2e, to appear in J. Amer. Math. Soc

Keywords

Algebraic Geometry, 14N35 (Primary) 14M15, 14N15, 05E15 (Secondary)

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/67898

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0306388
 http://arxiv.org/abs/math/0306388

Collections

arXiv