Fixed divisors on hyperkähler manifolds
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915618457911296 |
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| author | Agostini, Daniele Höring, Andreas |
| author_facet | Agostini, Daniele Höring, Andreas |
| contents | Let $X$ be a hyperkähler manifold, and let $A$ be a nef and big divisor on $X$. We show that the fixed part of the linear system $|A|$ is reduced and as a consequence $|2A|$ is mobile. If $X$ has dimension four we also show that if the fixed part of $|A|$ is not empty, the mobile part induces a (rational) Lagrangian fibration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11226 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fixed divisors on hyperkähler manifolds Agostini, Daniele Höring, Andreas Algebraic Geometry 14J42, 14C20, 14J45, 14E30 Let $X$ be a hyperkähler manifold, and let $A$ be a nef and big divisor on $X$. We show that the fixed part of the linear system $|A|$ is reduced and as a consequence $|2A|$ is mobile. If $X$ has dimension four we also show that if the fixed part of $|A|$ is not empty, the mobile part induces a (rational) Lagrangian fibration. |
| title | Fixed divisors on hyperkähler manifolds |
| topic | Algebraic Geometry 14J42, 14C20, 14J45, 14E30 |
| url | https://arxiv.org/abs/2511.11226 |