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Kobayashi non-hyperbolicity and hyperk\"ahler manifolds

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Ljudmila Kamenova (Stony Brook) - SFB-Seminar (SFB Transregio 45): 'Cones of products'

What
  • SFB-Seminar
When Jun 03, 2014
from 04:15 pm to 05:15 pm
Where Bonn, Raum 0.011, Mathematik-Zentrum, Endenicher Allee 60
Contact Name Sachinidis
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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 has conjectured that this pseudometric vanishes on Calabi-Yau manifolds. Using ergodicity of complex structures, we prove Kobayashi's conjecture for any hyperk\"ahler manifold that admits a deformation with a Lagrangian fibration, if its Picard rank is not maximal. We shall discuss the proof of Kobayashi's conjecture for K3 surfaces and for certain hyperk\"ahler manifolds. These results are joint with S. Lu and M. Verbitsky.