D. Greb

Arakelov inequalities and characterization of totally geodesic ball quotients in $\mathcal{A}_g$

We establish an Arakelov inequality for variations of Hodge structures underlying families of principally polarized complex Abelian varieties. In the equality case, this leads to a numerical characterization of certain totally geodesic ball quotients inside the moduli space of Abelian varieties. Our result extends work...