Slope of Siegel modular forms: some geometric applications
Riccardo Salvati Manni
16-02-2023 - 14:15
Largo San Leonardo Murialdo, 1
We study the slope of modular forms on the Siegel space. We will recover known divisors of minimal slope for gleq 5 and we discuss the Kodaira dimension of the moduli space of principally polarized abelian varieties A_g (and eventually of the generalized Kuga's varieties). Moreover we illustrate the cone of moving divisors on A_g. Partly motivated by the generalized Rankin-Cohen bracket, we construct a non-linear holomorphic differential operator that sends Siegel modular forms to Siegel cusp forms, and we apply it to produce new modular forms. Our construction recovers the known divisors of minimal moving slope on A_g for small genera.