14 dec 2016 -- 14:30
Aula di Consiglio, Dip.Matematica, Università "La Sapienza", Roma
Abstract.
In this talk I will present some of the results of my Ph.D. thesis.
I will show some geometric applications of the theory of Siegel modular forms.
The first result I will present is a generalization of Mukai's result about the existence of a degree 8 automorphism of the Igusa quartic, a compactification of a moduli space of principally polarized abelian varieties with some extra structure.
Although I will mostly talk about Siegel modular forms as tools for the study of complex Abelian varieties and their moduli spaces, they also represent an interesting and rich subject by themselves in the theory of automorphic forms. Indeed I will give a new construction of vector-valued modular forms from scalar-valued ones involving some multi-linear algebra constructions. As an application I will show the identity of two remarkable spaces of vector-valued modular forms. Finally I will give a new characterization of the locus of decomposable principally polarized abelian varieties through the image of the smooth 2-torsion points on the theta divisor.