Kobayashi pseudometric on hyperkahler manifolds

Kamenova, Ljudmila; Lu, Steven S. Y. et Verbitsky, Misha (2014). « Kobayashi pseudometric on hyperkahler manifolds ». Journal of the London Mathematical Society, 90(2), pp. 436-450.

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Résumé

The Kobayashi pseudometric on a complex manifold M is the maximal pseudometric such that any holomorphic map from the Poincaré disk to M is distance-decreasing. Kobayashi has conjectured that this pseudometric vanishes on Calabi-Yau manifolds. Using ergodicity of complex structures, we prove this result for any hyperk¨ahler manifold if it admits a deformation with a Lagrangian fibration, and its Picard rank is not maximal. The SYZ conjecture claims that any parabolic nef line bundle on a deformation of a given hyperkähler manifold is semi-ample. We prove that the Kobayashi pseudometric vanishes for all hyperkähler manifolds satisfying the SYZ property. This proves the Kobayashi conjecture for K3 surfaces and their Hilbert schemes.

Type:	Article de revue scientifique
Mots-clés ou Sujets:	Several complex variables and analytic spaces, Complex manifolds, Hyperbolic and Kobayashi hyperbolic manifolds
Unité d'appartenance:	Faculté des sciences > Département de mathématiques
Déposé par:	Steven Lu
Date de dépôt:	09 juin 2016 13:40
Dernière modification:	27 juin 2016 16:01
Adresse URL :	http://archipel.uqam.ca/id/eprint/8605

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