Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms
Algebraic Geometry
2026-03-09 v5 Mathematical Physics
Classical Analysis and ODEs
math.MP
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.
Keywords
Cite
@article{arxiv.2112.07182,
title = {Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms},
author = {Dingxin Zhang and Jie Zhou},
journal= {arXiv preprint arXiv:2112.07182},
year = {2026}
}