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Journal Articles Journal de l'École polytechnique — Mathématiques Year : 2021

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.

Dates and versions

hal-02998488 , version 1 (10-11-2020)

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Cite

Andreas Höring, Fabrizio Anella. Twisted cotangent bundles of Hyperk\"ahler manifolds. Journal de l'École polytechnique — Mathématiques, 2021, 8, pp.1429-1457. ⟨10.5802/jep.175⟩. ⟨hal-02998488⟩
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