Twisted cotangent bundle of Hyperkähler manifolds  (with an appendix by Simone Diverio)

Fabrizio Anella; Andreas Höring

doi:10.5802/jep.175

Twisted cotangent bundle of Hyperkähler manifolds (with an appendix by Simone Diverio)
[Faisceau cotangent tordu des variétés hyperkählériennes]

Fabrizio Anella ¹ ; Andreas Höring ²

¹ Mathematisches Institut, Universität Bonn Endenicher Allee 60, 53115 Bonn, Germany
² Université Côte d’Azur, CNRS, LJAD 06108 Nice cedex 02, France

Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 1429-1457.

Résumé
Abstract

Soit $X$ une variété hyperkählérienne, et $H$ un diviseur ample sur $X$ . Nous donnons une borne inférieure en fonction de la forme de Beauville-Bogomolov-Fujiki $q (H)$ pour la pseudo-effectivité du faisceau cotangent tordu $Ω_{X} \otimes H$ . Si $X$ est équivalente par déformation au schéma de Hilbert ponctuel d’une surface K3, cette borne inférieure peut être calculée explicitement et nous étudions son optimalité.

Let $X$ be a Hyperkähler manifold, and let $H$ be an ample divisor on $X$ . We give a lower bound in terms of the Beauville–Bogomolov–Fujiki form $q (H)$ for the pseudoeffectivity of the twisted cotangent bundle $Ω_{X} \otimes H$ . If $X$ is deformation equivalent to the punctual Hilbert scheme of a K3 surface, the lower bound can be written down explicitly and we study its optimality.

Reçu le : 2021-01-27
Accepté le : 2021-08-04
Publié le : 2021-09-03

DOI : 10.5802/jep.175

Classification : 14J42, 14J60, 14J28
Keywords: Hyperkähler manifold, cotangent bundle, positivity of vector bundles
Mot clés : Variété hyperkählérienne, fibré cotangent, positivité des fibrés vectoriels

Affiliations des auteurs :

Fabrizio Anella ¹ ; Andreas Höring ²

¹ Mathematisches Institut, Universität Bonn Endenicher Allee 60, 53115 Bonn, Germany
² Université Côte d’Azur, CNRS, LJAD 06108 Nice cedex 02, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Twisted cotangent bundle of {Hyperk\"ahler~manifolds}  (with an appendix by {Simone} {Diverio)}},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
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Fabrizio Anella; Andreas Höring. Twisted cotangent bundle of Hyperkähler manifolds  (with an appendix by Simone Diverio). Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 1429-1457. doi : 10.5802/jep.175. https://jep.centre-mersenne.org/articles/10.5802/jep.175/

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