Algebra/Topology seminar

Speaker: Xiyan Zhong

Title: Rigidity of the period map up to finite covers.

Abstract: The period map is an important holomorphic map from the moduli space M_g of genus g curves to the moduli space A_g of g-dimensional principally polarized abelian varieties, sending a curve to its Jacobian. Benson Farb proved that the period map is the unique nonconstant holomorphic map from M_g to A_h for h at most g. In recent work, we study holomorphic maps from a certain finite cover R_g of M_g to A_h for h at most g, and prove that the unique nonconstant holomorphic map from R_g to A_h is the lift of the period map to R_g. The proof proceeds by first classifying linear representations of certain finite-index subgroups of the mapping class group.