28 may 2014 -- 10:00
Sala Conferenze (Puteano, Centro De Giorgi, Pisa)
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.