On the group of automorphisms of Horikawa surfaces
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 irreduci...
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| Language: | English |
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Académie des sciences
2024-05-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.546/ |
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| author | Lorenzo, Vicente |
| author_facet | Lorenzo, Vicente |
| author_sort | Lorenzo, Vicente |
| collection | DOAJ |
| description | 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 $\mathbb{Z}_2$. |
| format | Article |
| id | doaj-art-eb2f62a6daae4966be1b7dce4ace2e76 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-eb2f62a6daae4966be1b7dce4ace2e762025-02-07T11:19:53ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-05-01362G323724410.5802/crmath.54610.5802/crmath.546On the group of automorphisms of Horikawa surfacesLorenzo, Vicente0https://orcid.org/0000-0003-2077-6095Telematic Engineering Department, Universidad Carlos III de Madrid, Avenida de la Universidad 30, Leganés (Madrid), Spain.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 $\mathbb{Z}_2$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.546/ |
| spellingShingle | Lorenzo, Vicente On the group of automorphisms of Horikawa surfaces Comptes Rendus. Mathématique |
| title | On the group of automorphisms of Horikawa surfaces |
| title_full | On the group of automorphisms of Horikawa surfaces |
| title_fullStr | On the group of automorphisms of Horikawa surfaces |
| title_full_unstemmed | On the group of automorphisms of Horikawa surfaces |
| title_short | On the group of automorphisms of Horikawa surfaces |
| title_sort | on the group of automorphisms of horikawa surfaces |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.546/ |
| work_keys_str_mv | AT lorenzovicente onthegroupofautomorphismsofhorikawasurfaces |