Speaker：Matteo Penegini (Università degli Studi di Pavia)

Time：2025-12-10 10:00

Location：Conference Room S204 at Experiment Building at Haiyun Campus

Abstract:

To extend the Beauville-Bogomolov decomposition theorem, we need to define the singular versions of irreducible holomorphic symplectic manifolds, known as "singular irreducible symplectic varieties." These are compact, connected complex varieties with canonical singularities that possess a holomorphic symplectic form σ on the smooth locus, and for which every finite quasi-étale covering has its algebra of reflexive forms spanned by the reflexive pull-back of σ. We classify all singular irreducible symplectic surfaces, which are essentially contractions of ADE configurations of curves on K3 surfaces. We describe the families of these surfaces, categorizing them into two classes: those that do not admit any quasi-étale coverings, and those that do, necessarily with a K3 surface. Finally, we briefly discuss the Hilbert scheme of two points on these surfaces.