Time
16:30--17:30pm, Friday, 7/24, 2009

Abstract

Let (X,L) be a polarized algebraic manifold. I have recently proved that the Mabuchi energy of (X,L) is bounded from below along all degenerations if and only if the Hyperdiscriminant polytope (of X) contains the Chow polytope with respect to the various Kodaira embeddings . In particular I can show that the asymptotic behavior of the Mabuchi energy along any degeneration is logarithmic (previously only known for hypersurfaces and curves), and the coefficient of blow up is an integer-moreover, this integer is given by minimizing the integral linear functional corresponding to the degeneration over the two polyhedra of the title.