On the group of automorphisms of Horikawa surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911873291517952 |
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| author | Lorenzo, V. |
| author_facet | Lorenzo, V. |
| contents | Minimal algebraic surfaces of general type $X$ such that $K^2_X=2χ(\mathcal{O}_X)-6$ 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 $(K^2, χ)$ such that $K^2=2χ-6$, every irreducible component of Gieseker's moduli space $\mathfrak{M}_{K^2,χ}$ contains an open subset consisting of surfaces with group of automorphisms isomorphic to $\mathbb{Z}_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_04890 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the group of automorphisms of Horikawa surfaces Lorenzo, V. Algebraic Geometry 14J29 Minimal algebraic surfaces of general type $X$ such that $K^2_X=2χ(\mathcal{O}_X)-6$ 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 $(K^2, χ)$ such that $K^2=2χ-6$, every irreducible component of Gieseker's moduli space $\mathfrak{M}_{K^2,χ}$ contains an open subset consisting of surfaces with group of automorphisms isomorphic to $\mathbb{Z}_2$. |
| title | On the group of automorphisms of Horikawa surfaces |
| topic | Algebraic Geometry 14J29 |
| url | https://arxiv.org/abs/2201.04890 |