Fixed divisors on hyperkähler manifolds
Abstract Let be a hyperkähler manifold, and let be a nef and big divisor on . We show that the fixed part of the linear system is reduced, and as a consequence, that is mobile. If has dimension 4, we also show that if the fixed part of is not empty, the mobile part induces a (rational) Lagrangian fibration.
Authors
- Andreas Höring (ORCID: https://orcid.org/0000-0001-7747-8238)
- Daniele Agostini (ORCID: https://orcid.org/0000-0002-9919-5391)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Institut de Physique de Nice (FR)
- University of Tübingen (DE)
Publication Details
- Journal
- Proceedings of the London Mathematical Society
- Published
- 2026-04-01
- DOI
- https://doi.org/10.1112/plms.70152
- Primary Topic
- Geometry and complex manifolds
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Deutsche Forschungsgemeinschaft
- Agence Nationale de la Recherche