On the group of automorphisms of Horikawa surfaces

V. Lorenzo

On the group of automorphisms of Horikawa surfaces

Algebraic Geometry 2024-05-14 v2

Authors: V. Lorenzo

Abstract

Minimal algebraic surfaces of general type $X$ such that $K^2_X=2\chi(\mathcal{O}_X)-6$ are called Horikawa surfaces. In this note the group of automorphisms of Horikawa surfaces is studied. The main result states that given an admissible pair $(K^2, \chi)$ such that $K^2=2\chi-6$ , every irreducible component of Gieseker's moduli space $\mathfrak{M}_{K^2,\chi}$ contains an open subset consisting of surfaces with group of automorphisms isomorphic to $\mathbb{Z}_2$ .

Keywords

Horikawa surfaces automorphism group minimal algebraic surfaces of general type Gieseker moduli space admissible pair irreducible component

Cite

@article{arxiv.2201.04890,
  title  = {On the group of automorphisms of Horikawa surfaces},
  author = {V. Lorenzo},
  journal= {arXiv preprint arXiv:2201.04890},
  year   = {2024}
}

Comments

Some changes following referee's report. Final version to appear in Comptes Rendus Math\'ematique. 12 pages

On the group of automorphisms of Horikawa surfaces

Abstract

Keywords

Cite

Comments

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