The Hodge diamond of O'Grady's 6-dimensional example

TL;DR

This paper constructs and analyzes a specific 6-dimensional irreducible holomorphic symplectic manifold, revealing its Hodge structure by relating it to a K3$^{[3]}$-type manifold and a birational involution.

Contribution

It provides a geometric realization of O'Grady's 6-dimensional example as a quotient of a known IHS manifold, enabling explicit computation of its Hodge numbers.

Findings

Realization of O'Grady's 6-dimensional manifold as a quotient.

Explicit computation of Hodge numbers for the example.

Insight into the structure of irreducible holomorphic symplectic manifolds.

Abstract

We realize O'Grady's six dimensional example of irreducible holomorphic symplectic manifold as a quotient of an IHS manifold of K3$^{[3]}$-type by a birational involution, thereby computing its Hodge numbers.