Seminari del Dipartimento



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.

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org: Turchet Amos