No cohomologically trivial non-trivial automorphism of generalized Kummer manifolds

Abstract

We prove that the natural representaion, on the total Betti cohomolgy group, of the automorphism group of a hyperkähler manifold deformation equivalent to a generalized Kummer manifold is faithful. This is a sort of generalization of an earlier work of Beauville and a recent work of Boissére, Nieper-Wisskirchan and Sarti, concerning the representation on the second cohomology group.

final form to appear in Nagoya Math. J

References in corpus (2)

• Mapping class group and global Torelli theorem for hyperkahler manifolds: an erratum
• On natural deformations of symplectic automorphisms of manifolds of K3^[n] type

Cited by in corpus (7)

• On the existence of universal families of marked irreducible holomorphic symplectic manifolds
• Surfaces of general type with q=2 are rigidified
• Automorphisms of generalised Kummer fourfolds
• k-symplectic structures and absolutely trianalytic subvarieties in hyperkahler manifolds
• Automorphisms of surfaces of general type with q>=2 acting trivially in cohomology
• Integral cohomology of the Generalized Kummer fourfold
• Counting real rational curves on K3 surfaces