On the Andre motive of certain irreducible symplectic varieties

TL;DR

This paper demonstrates that the Andre motive of certain irreducible symplectic varieties, deformation equivalent to Hilbert schemes on K3 surfaces, is generated by its degree-two motive, revealing structural insights into their motives.

Contribution

It establishes that the Andre motive of these symplectic varieties is generated by its degree-two component, advancing understanding of their motive structure.

Findings

Andre motive of these varieties is generated by degree-two motive

Provides new structural insight into motives of symplectic varieties

Connects deformation equivalence with motive generation

Abstract

We show that the Andre motive of an irreducible, symplectic variety, which is deformation equivalent to the Hilbert scheme of points on a K3 surface, is an object the category generated by its motive truncated in degree two.