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- W2962727703 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 Gottsche's formula for the Hilbert scheme of $g$ points on a surface, we find precise agreement of our results with the proposal recently made by Gopakumar and Vafa(hep-th/9812127)." @default.
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- W2962727703 date "1999-01-01" @default.
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- W2962727703 title "Holomorphic anomaly equation and BPS state counting of rational elliptic surface" @default.
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- W2962727703 doi "https://doi.org/10.4310/atmp.1999.v3.n1.a7" @default.
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