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2014
- handle: 10670/1.2sc5g2
- 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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http://archipel.uqam.ca/8605/
Ce document est lié à :
http://dx.doi.org/10.1112/jlms/jdu038
Ce document est lié à :
doi:10.1112/jlms/jdu038
Mots-clés
Several complex variables and analytic spaces Complex manifolds Hyperbolic and Kobayashi hyperbolic manifoldsSujets proches
ConjectureCiter ce document
Ljudmila Kamenova et al., « Kobayashi pseudometric on hyperkahler manifolds », UQAM Archipel : articles scientifiques, ID : 10670/1.2sc5g2
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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.