Cohomologically or numerically trivial automorphisms of surfaces of general type
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908788812939264 |
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| author | Catanese, Fabrizio Frapporti, Davide |
| author_facet | Catanese, Fabrizio Frapporti, Davide |
| contents | Our main result is the determination of the respective groups $ Aut_\mathbb{Z}(S) $ of cohomologically trivial automorphisms and $ Aut_\mathbb{Q}(S) $ of numerically trivial automorphisms for the reducible fake quadrics, that is, the surfaces $S$ isogenous to a product with $q=p_g=0$.
In this way we produce new record winning examples: a surface $S$ with $|Aut_\mathbb{Q}(S)| =192$, and a surface whose cohomology has torsion with nontrivial $ Aut_\mathbb{Z}(S) \cong \mathbb{Z}/2.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18389 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cohomologically or numerically trivial automorphisms of surfaces of general type Catanese, Fabrizio Frapporti, Davide Algebraic Geometry Complex Variables 14J50, 14J80, 14H30, 14F99, 32L05, 32M99, 32Q15, 32Q55 Our main result is the determination of the respective groups $ Aut_\mathbb{Z}(S) $ of cohomologically trivial automorphisms and $ Aut_\mathbb{Q}(S) $ of numerically trivial automorphisms for the reducible fake quadrics, that is, the surfaces $S$ isogenous to a product with $q=p_g=0$. In this way we produce new record winning examples: a surface $S$ with $|Aut_\mathbb{Q}(S)| =192$, and a surface whose cohomology has torsion with nontrivial $ Aut_\mathbb{Z}(S) \cong \mathbb{Z}/2.$ |
| title | Cohomologically or numerically trivial automorphisms of surfaces of general type |
| topic | Algebraic Geometry Complex Variables 14J50, 14J80, 14H30, 14F99, 32L05, 32M99, 32Q15, 32Q55 |
| url | https://arxiv.org/abs/2601.18389 |