# Twisted cotangent bundles of Hyperk\"ahler manifolds

Abstract : Let $X$ be a Hyperk\"ahler manifold, and let $H$ be an ample divisor on $X$. We give a lower bound in terms of the Beauville-Bogomolov form $q(H)$ for the twisted cotangent bundle $\Omega_X \otimes H$ to be pseudoeffective. If $X$ is deformation equivalent to the Hilbert scheme of a K3 surface the lower bound can be written down explicitly and we study its optimality.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.univ-cotedazur.fr/hal-02998488
Contributor : Andreas Höring <>
Submitted on : Tuesday, November 10, 2020 - 3:17:03 PM
Last modification on : Thursday, November 12, 2020 - 12:11:43 PM

### Identifiers

• HAL Id : hal-02998488, version 1
• ARXIV : 1906.11528

### Citation

Andreas Höring, Fabrizio Anella. Twisted cotangent bundles of Hyperk\"ahler manifolds. 2020. ⟨hal-02998488⟩

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