Cohomology and Andr\'e motives of hyperk\"ahler orbifolds

TL;DR

This paper explores the cohomology and motives of hyperk"ahler orbifolds, demonstrating that their Andr"e motives are generally abelian, using Lie algebra actions on cohomology.

Contribution

It extends the study of hyperk"ahler manifolds to orbifolds, showing that their Andr"e motives are abelian, a novel insight in the field.

Findings

Andr"e motives of hyperk"ahler orbifolds tend to be abelian

Lie algebra actions help analyze cohomology of orbifolds

Extension of hyperk"ahler manifold techniques to orbifolds

Abstract

One of the main tools for the study of compact hyperk\"ahler manifolds is the natural action of the Looijenga-Lunts-Verbitsky Lie algebra on the cohomology of such manifolds. This also applies to the mildly singular holomorphic symplectic varieties - hyperk\"ahler orbifolds, allowing us to prove that Andr\'e motives of such orbifolds tend to be abelian.