Soit une variété hyperkählérienne, et un diviseur ample sur . Nous donnons une borne inférieure en fonction de la forme de Beauville-Bogomolov-Fujiki pour la pseudo-effectivité du faisceau cotangent tordu . Si 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 be a Hyperkähler manifold, and let be an ample divisor on . We give a lower bound in terms of the Beauville–Bogomolov–Fujiki form for the pseudoeffectivity of the twisted cotangent bundle . If 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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Keywords: Hyperkähler manifold, cotangent bundle, positivity of vector bundles
Mot clés : Variété hyperkählérienne, fibré cotangent, positivité des fibrés vectoriels
@article{JEP_2021__8__1429_0, author = {Anella, Fabrizio and H\"oring, Andreas}, 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}, volume = {8}, year = {2021}, doi = {10.5802/jep.175}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jep.175/} }
TY - JOUR AU - Anella, Fabrizio AU - Höring, Andreas TI - Twisted cotangent bundle of Hyperkähler manifolds (with an appendix by Simone Diverio) JO - Journal de l’École polytechnique — Mathématiques PY - 2021 SP - 1429 EP - 1457 VL - 8 PB - Ecole polytechnique UR - http://www.numdam.org/articles/10.5802/jep.175/ DO - 10.5802/jep.175 LA - en ID - JEP_2021__8__1429_0 ER -
%0 Journal Article %A Anella, Fabrizio %A Höring, Andreas %T Twisted cotangent bundle of Hyperkähler manifolds (with an appendix by Simone Diverio) %J Journal de l’École polytechnique — Mathématiques %D 2021 %P 1429-1457 %V 8 %I Ecole polytechnique %U http://www.numdam.org/articles/10.5802/jep.175/ %R 10.5802/jep.175 %G en %F JEP_2021__8__1429_0
Anella, Fabrizio; Höring, Andreas. 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. http://www.numdam.org/articles/10.5802/jep.175/
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