Parabolic automorphisms of hyperk{ä}hler manifolds: Orbits and Betti maps
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866929695641042944 |
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| author | Amerik, Ekaterina Cantat, Serge |
| author_facet | Amerik, Ekaterina Cantat, Serge |
| contents | We study parabolic automorphisms of irreducible holomorphically symplectic manifolds with a lagrangian fibration. Such automorphisms are (possibly up to taking a power) fiberwise translations on smooth fibers, and their orbits in a general fiber are dense ([1]). We provide a simple proof that the associated Betti map is of maximal rank, in particular, the set of fibers where the induced translation is of finite order is dense as well. R{É}SUM{É}. Nous {é}tudions les automorphismes paraboliques des vari{é}t{é}s symplectiques holomorphes qui sont irr{é}ductibles et projectives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01149 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parabolic automorphisms of hyperk{ä}hler manifolds: Orbits and Betti maps Amerik, Ekaterina Cantat, Serge Algebraic Geometry We study parabolic automorphisms of irreducible holomorphically symplectic manifolds with a lagrangian fibration. Such automorphisms are (possibly up to taking a power) fiberwise translations on smooth fibers, and their orbits in a general fiber are dense ([1]). We provide a simple proof that the associated Betti map is of maximal rank, in particular, the set of fibers where the induced translation is of finite order is dense as well. R{É}SUM{É}. Nous {é}tudions les automorphismes paraboliques des vari{é}t{é}s symplectiques holomorphes qui sont irr{é}ductibles et projectives. |
| title | Parabolic automorphisms of hyperk{ä}hler manifolds: Orbits and Betti maps |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2502.01149 |