Twisted cotangent bundle of Hyperkähler manifolds (with an appendix by Simone Diverio)
[Faisceau cotangent tordu des variétés hyperkählériennes]
Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 1429-1457.

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 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 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.

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DOI : https://doi.org/10.5802/jep.175
Classification : 14J42,  14J60,  14J28
Mots clés : Variété hyperkählérienne, fibré cotangent, positivité des fibrés vectoriels
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     author = {Fabrizio Anella and Andreas H\"oring},
     title = {Twisted cotangent bundle of {Hyperk\"ahler~manifolds}  (with an appendix by {Simone} {Diverio)}},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
     pages = {1429--1457},
     publisher = {\'Ecole polytechnique},
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     year = {2021},
     doi = {10.5802/jep.175},
     language = {en},
     url = {https://jep.centre-mersenne.org/articles/10.5802/jep.175/}
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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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