Holomorphic Anomaly Equation and BPS State Counting of Rational Elliptic Surface
High Energy Physics - Theory
2008-11-26 v4 Algebraic Geometry
Abstract
We consider the generating function (prepotential) for Gromov-Witten invariants of rational elliptic surface. We apply the local mirror principle to calculate the prepotential and prove a certain recursion relation, holomorphic anomaly equation, for genus 0 and 1. We propose the holomorphic anomaly equation for all genera and apply it to determine higher genus Gromov-Witten invariants and also the BPS states on the surface. Generalizing G\"ottsche's formula for the Hilbert scheme of points on a surface, we find precise agreement of our results with the proposal recently made by Gopakumar and Vafa(hep-th/9812127).
Keywords
Cite
@article{arxiv.hep-th/9901151,
title = {Holomorphic Anomaly Equation and BPS State Counting of Rational Elliptic Surface},
author = {S. Hosono and M. -H. Saito and A. Takahashi},
journal= {arXiv preprint arXiv:hep-th/9901151},
year = {2008}
}
Comments
27 pages, uses harvmac.tex; published form with note added in proof