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On Kobayashi's conjecture for K3 surfaces and hyperk\"ahler manifolds"

Presented by: 
L Kamenova Stony Brook University
Monday 3rd August 2015 - 16:00 to 17:00
INI Seminar Room 2
The Kobayashi pseudometric on a complex manifold M is the maximal pseudometric such that any holomorphic map from the Poincare disk to M is distance-decreasing. Kobayashi conjectured that this pseudometric vanishes on Calabi-Yau manifolds. Using ergodicity of complex structures, we prove this conjecture for any hyperkahler manifold that admits a deformation with a Lagrangian fibration, and its Picard rank is not maximal. For hyperkahler manifolds with maximal Picard rank we need an extra assumption, the SYZ conjecture. We shall discuss the proof of Kobayashi's conjecture for K3 surfaces and for certain hyperkahler manifolds. These results are joint with S. Lu and M. Verbitsky.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons