Seminar| Institute of Mathematical Sciences
Time：Friday, June 18th, 2021, 11:00-12:00
Location：R408, IMS
Speaker: Xin Dong, University of Connecticut
Abstract:We study the behaviors of the relative Bergman kernel metrics on holomorphic families of degenerating hyperelliptic Riemann surfaces and their Jacobian varieties. Near a node or cusp, we obtain precise asymptotic formulas with explicit coefficients. In general the Bergman kernels on a given cuspidal family do not always converge to that on the regular part of the limiting surface, which is different from the nodal case. Information on both the singularity and complex structure contributes to various asymptotic behaviors of the Bergman kernel. Our method involves the classical Taylor expansion for Abelian differentials and period matrices. This talk is based on arXiv: 2005.11826.