CRM: Centro De Giorgi
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Seminari di Sistemi Dinamici Olomorfi 2013-2014

seminar: Convergence of Bergman metrics on Kähler and symplectic manifolds

speaker: Xiaonan MA (Institute de Mathématiques de Jussieu, Paris)

abstract: For a compact K"ahler manifold \(X\) endowed with a Hermitian positive holomorphic positive line bundle \(L\), The Bergman metric at level \(p\) is defined as the rescaled induced Fubini-Study metric for the Kodaira embedding of \(X\) into the projective space associated to \(L^p\). A theorem of Tian said that this Bergman metric will converge to the original Käher form. We will explain some of its implications on the zero of radom sections of \(L^p\). Then we will explain a symplectic analogue of Tian's theorem with optimal convergence speed.

Wed 28 May, 10:00 - 11:15, Sala Conferenze Centro De Giorgi
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