Gromov-Witten invariants on Grassmannians
Algebraic Geometry
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0306388,
title = {Gromov-Witten invariants on Grassmannians},
author = {Anders Skovsted Buch and Andrew Kresch and Harry Tamvakis},
journal= {arXiv preprint arXiv:math/0306388},
year = {2007}
}
Comments
15 pages, LaTeX2e, to appear in J. Amer. Math. Soc