A question of Doctor Malte Wandel on automorphisms of the punctural Hilbert schemes of K3 surfaces

Abstract

We present a sufficient condition for the punctural Hilbert scheme of length two of a K3 surface with finite automorphism group to have automorphism group of infinite order in geometric terms (Theorem 2.1). We then give concrete examples (Theorem 1.2). We also discuss about Mori dream space (MDS) structures under an extermal crepant resolution (Theorems 1.2, 5.2, 4.1) from the viewpoint of automorphisms. These affirmatively answer a question of Doctor Malte Wandel.

14pages, expanded semi-final version to be submitted

References in corpus (1)

• A proof of the Kawamata-Morrison Cone Conjecture for holomorphic symplectic varieties of K3^[n] or generalized Kummer deformation type

Cited by in corpus (3)

• Automorphisms of Hilbert schemes of points on surfaces
• Universal covering calabi-yau manifolds of the Hilbert schemes of n points of Enriques surfaces
• Mori Dream Spaces extremal contractions of K3 surfaces