Title: Partial Bergman kernels and stability
Speaker: Michael Singer
Speaker Info: Edinburgh
Brief Description:
Special Note:
Abstract:
The Bergman kernel on a compact Kaehler manifold is the Schwartz kernel of the L^2 projection onto the space of holomorphic sections of some ample line bundle L. Much is known about the asymptotic behaviour of the Bergman kernel for high powers of the bundle L. In this talk, we will consider the `partial' projection onto the subspace of sections vanishing to order lk along a submanifold. Restricting to the toric case, we will prove the existence of a distributional asymptotic expansion for the corresponding partial density function (the value of the kernel on the diagonal), at least to leading order, and indicate an application to the study of stability of the polarized manifold (M,L).Date: Monday, October 3, 2011