Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms
- Resource Type
- Working Paper
- Authors
- Zhang, Dingxin; Zhou, Jie
- Source
- Subject
- Mathematics - Algebraic Geometry
Mathematical Physics
Mathematics - Classical Analysis and ODEs
- Language
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.
Comment: numerous typos fixed