Examples of irreducible symplectic varieties

Abstract

Irreducible symplectic manifolds are one of the three building blocks of compact Kähler manifolds with numerically trivial canonical bundle by the Beauville-Bogomolov decomposition theorem. There are several singular analogues of irreducible symplectic manifolds, in particular in the context of compact Kähler orbifolds, and in the context of normal projective varieties with canonical singularities. In this paper we will collect their definitions, analyze their mutual relations and provide a list of known examples.

To appear in the Springer INdAM Series volume related to the conference 'Birational Geometry and Moduli Spaces' held in Rome