Open Torelli locus and complex ball quotients

TL;DR

This paper investigates the non-existence of certain complex ball quotients within the Torelli locus of moduli spaces of Abelian varieties using analytic methods.

Contribution

It provides new results on the non-existence of totally geodesic complex ball quotients in the open Torelli locus.

Findings

Proves non-existence of certain complex ball quotients in Torelli locus

Uses analytic techniques to establish geometric constraints

Contributes to understanding the structure of moduli spaces

Abstract

We study the problem of non-existence of totally geodesic complex ball quotients in the open Torelli locus in a moduli space of principally polarized Abelian varieties using analytic techniques.