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arXiv · 2511.11226

Fixed divisors on hyperk\"ahler manifolds

Daniele Agostini·Andreas Höring
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Abstract

Let $X$ be a hyperk\"ahler 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.

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Daniele Agostini, Andreas Höring. 2025-11-14. Fixed divisors on hyperk\"ahler manifolds. https://arxiv.org/abs/2511.11226

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