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

2014/02/18 by Keiji Oguiso, Oguiso, Keiji · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1402.4228

14pages, expanded semi-final version to be submitted

openalex publication_date 2014/02/18 · arxiv created 2014/12/25 · arxiv updated 2014/12/30 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28

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.

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