2021/12/14 by Zhang, Dingxin, Zhou, Jie
#Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2112.07182
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.