1998/06/23 by Rahul Pandharipande, Pandharipande, Rahul
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.math/9806133
33 pages, Latex2e
arxiv created 1998/06/23 · arxiv updated 2009/11/30
This article accompanies my June 1998 seminaire Bourbaki talk on Givental's work. After a quick review of descendent integrals in Gromov-Witten theory, I discuss Givental's formalism relating hypergeometric series to solutions of quantum differential equations arising from hypersurfaces in projective space. A particular case of this relationship is a proof of the Mirror prediction for the numbers of rational curves on the Calabi-Yau quintic 3-fold. The approach taken here is entirely algebro-geometric and relies upon a localization formula on the moduli space of stable genus 0 maps to projective space. A different proof of the quintic Mirror prediction may be found in the work of Lian, Liu, and Yau.