Induced birational transformations on O'Grady's sixfolds

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 $O{G}_6$ 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--Saccá birational model of manifolds of $O{G}_6$ 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.

arXiv commentMain results are extended to birational transformations. Section 5 has been added. To appear in Journal of the London Mathematical Society

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Cited by in corpus (1)

• Symplectic birational transformations of finite order on O'Grady's sixfolds