Genus one GW invariants of quintic threefolds via MSP localization
Huai-Liang Chang, Shuai Guo, Wei-Ping Li, Jie Zhou
TL;DR
This paper applies a localization algorithm to compute genus one Gromov-Witten invariants of quintic Calabi-Yau threefolds, revealing new hypergeometric identities and advancing enumerative geometry methods.
Contribution
It extends the MSP localization algorithm to genus one, providing explicit computations and new identities in the context of quintic threefolds.
Findings
Computed genus one Gromov-Witten invariants for quintic threefolds.
Discovered new hypergeometric series identities.
Demonstrated effectiveness of MSP localization in genus one case.
Abstract
The moduli stack of Mixed Spin P-fields (MSP) provides an effective algorithm to evaluate all genus Gromov-Witten invariants of quintic Calabi-Yau threefolds. This paper is to apply the algorithm in genus one case. We use the localization formula, the proposed algorithm in [CLLL1, CLLL2], and Zinger's packaging technique to compute the genus one Gromov-Witten invariants of quintic Calabi-Yau threefolds. New hypergeometric series identities are also discovered in the process.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds