Lars Wüste-Schmülling: Noether–Lefschetz Cycles on A_g

Abstract:

For the moduli space of principally polarized abelian varieties, Canning, Molcho, Oprea, and Pandharipande defined a tautological projection from \(CH(A_g)\) to its tautological subring. A natural question is to compute the tautological projections of interesting cycles on \(A_g\). In this talk, I will discuss work of Aitor Iribar López, who computed the tautological projections of all Noether–Lefschetz cycles using level structures. I will explain the main ideas of his approach, as well as the argument showing that the tautological projection is a ring homomorphism when restricted to cycles supported on the Noether–Lefschetz locus.