Hodge structure of O'Grady's singular moduli spaces

TL;DR

This paper studies the Hodge structures of O'Grady's singular symplectic varieties, computes their Betti numbers and Euler characteristic, and shows they lack finite quotient singularities, addressing a specific open question.

Contribution

It provides the first detailed analysis of the Hodge structures and topological invariants of O'Grady's six and ten dimensional examples, clarifying their singularity properties.

Findings

Computed Betti numbers and Euler characteristic of the varieties.

Proved these varieties do not have finite quotient singularities.

Enhanced understanding of the topology of singular irreducible symplectic varieties.

Abstract

We investigate the Hodge structure of the singular O'Grady's six and ten dimensional examples of irreducible symplectic varieties. In particular, we compute some of their Betti numbers and their Euler characteristic. As consequence, we deduce that these varieties do not have finite quotient singularities answering a question of Bakker and Lehn.