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Automorphisms of Hilbert schemes of Cayley's K3 surfaces

Kwangwoo Lee

Abstract

We prove that the automorphism group of Hilbert square of a Cayley's K3 surface of Picard number 2 is the free product of three cyclic groups of order two. The generators are three Beauville involutions.

Automorphisms of Hilbert schemes of Cayley's K3 surfaces

Abstract

We prove that the automorphism group of Hilbert square of a Cayley's K3 surface of Picard number 2 is the free product of three cyclic groups of order two. The generators are three Beauville involutions.
Paper Structure (6 sections, 12 theorems, 40 equations)

This paper contains 6 sections, 12 theorems, 40 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Hilbert squares of K3 surfaces
  4. Hyperbolic geometry
  5. Proof
  6. Proof of Theorem \ref{['main theorem1']}

Key Result

Theorem 1.1

$\operatorname{Aut}(X^{[2]})\cong \langle \iota_0,\iota_1,\iota_2\rangle\cong {\mathbb Z}_2\ast {\mathbb Z}_2\ast {\mathbb Z}_2$.

Theorems & Definitions (24)

  • Theorem 1.1
  • Remark 1.2
  • Lemma 2.1
  • proof
  • Theorem 2.2
  • Lemma 2.3
  • proof
  • Theorem 2.4
  • Definition 2.5
  • Theorem 2.6
  • ...and 14 more