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Ergodic complex structures and Kobayashi metric

Le : 29/01/2014 14h00
Par : Misha Verbitsky (HSE, Moscou)
Lieu : I 001
Lien web :
Résumé : Let M be a compact manifold. Consider the action of the diffeomorphism group Diff(M) on the (infinite-dimensional) space Comp(M) of complex structures. A complex structure is called ergodic if its Diff(M)-orbit is dense in the connected component of Comp(M). I will show that on a hyperkaehler manifold or a compact torus, a complex structure is ergodic unless its Picard rank is maximal. This result has many geometric consequences; for instance, it follows that the Kobayashi pseudometric on any K3 surface or the deformations of its Hilbert scheme vanishes, solving a longstanding conjecture by Kobayashi.