Induced birational transformations on O'Grady's sixfolds

TL;DR

This paper studies induced birational transformations on O'Grady's sixfolds, providing criteria to identify when such transformations are derived from automorphisms of underlying abelian surfaces or their quotients.

Contribution

It introduces the notion of induced birational transformations on OG6-type manifolds and establishes criteria for their origin from automorphisms or quotients, advancing understanding of their birational geometry.

Findings

Criteria for birationality to moduli spaces of sheaves on abelian surfaces

Conditions under which transformations are induced by surface automorphisms

Application of criteria in nonsymplectic cases

Abstract

We introduce the notion of induced birational transformations of irreducible holomorphic symplectic sixfolds of the sporadic deformation type discovered by O'Grady. We give a criterion to determine when a manifold of $OG_6$ type is birational to a moduli space of sheaves on an abelian surface. Then we determine when a birational transformation of the moduli space is induced by an automorphism of the abelian surface. Referring to the Mongardi--Rapagnetta--Sacc\'{a} birational model of manifolds of $OG_6$ type, we give a result to determine when a birational transformation is induced at the quotient. We give an application of these criteria in the nonsymplectic case.