Two Proofs of a Conjecture of Hori and Vafa

Details Two Proofs of a Conjecture of Hori and Vafa Two Proofs of a Conjecture of Hori and Vafa

2003-04-25

arxiv.org/abs/math/0304403v1

Mathematics

Algebraic Geometry

34 pages, no figures

Scientific paper

We give two proofs of a conjecture of Hori and Vafa which expresses the J-function (i.e, the generating function for 1-point descendant Gromov-Witten invariants) of a Grassmannian in terms of the J-function of a product of projective spaces. Similar relations are obtained for two-point descendants, and three-point (primary) Gromov-Witten invariants. As an application we prove Givental's "R-Conjecture" - hence the Virasoro conjecture - for Grassmannians.

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