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arXiv · 2112.07182

Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms

Dingxin Zhang·Jie Zhou
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Abstract

We study one-parameter deformations of Calabi-Yau type Fermat polynomial singularities along degree-one directions. We show that twisted sectors in the vanishing cohomology are components of automorphic forms for certain triangular groups. We prove consequentially that genus zero Gromov-Witten generating series of the corresponding Fermat Calabi-Yau varieties are components of automorphic forms. The main tools we use are mixed Hodge structures for quasi-homogeneous polynomial singularities, Riemann-Hilbert correspondence, and genus zero mirror symmetry.

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Dingxin Zhang, Jie Zhou. 2021-12-14. Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms. https://doi.org/10.4310/cntp.251030232422

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