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arxiv: 0710.0889 · v1 · submitted 2007-10-03 · 🧮 math.CO · math.AG

Some Properties of Hypergeometric Series Associated with Mirror Symmetry

classification 🧮 math.CO math.AG
keywords propertiescalabi-yaugenusgromov-wittenhypergeometricinvariantsmirrorseries
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We show that certain hypergeometric series used to formulate mirror symmetry for Calabi-Yau hypersurfaces, in string theory and algebraic geometry, satisfy a number of interesting properties. Many of these properties are used in separate papers to verify the BCOV prediction for the genus one Gromov-Witten invariants of a quintic threefold and more generally to compute the genus one Gromov-Witten invariants of any Calabi-Yau projective hypersurface.

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  1. Quasi-modularity and holomorphic anomaly equation for the twisted Gromov-Witten theory: $\mathcal{O}(3)$ over $\mathbb{P}^2$

    math.AG 2019-06 unverdicted novelty 4.0

    Proves quasi-modularity and derives holomorphic anomaly equation for twisted GW theory of O(3) over P².