A note on automorphisms and birational transformations of holomorphic symplectic manifolds

Abstract

We give a necessary and sufficient condition for an automorphism of the Hilbert scheme of points on a K3 surface (non necessarily algebraic) to be induced by an automorphism of the surface. We prove furthermore that the group of birational transformations of a projective irreducible holomorphic symplectic manifold is finitely generated.

New version in english. New title and a new result (see updated abstract). To appear in Proc. AMS

References in corpus (2)

• Intersection numbers of extremal rays on holomorphic symplectic varieties
• On an automorphism of $Hil{b}^{[2]}$ of certain K3 surfaces

Cited by in corpus (1)

• Higher dimensional Enriques varieties and automorphisms of generalized Kummer varieties