EVENT DETAILS AND ABSTRACT

Title: Hyperdiscriminant polytopes, Chow Polytopes, and K-energy asymptotics
Speaker: Sean Paul
Speaker Info: University of Wisconsin, Madison
Brief Description:
Special Note:
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. In particular, the asymptotic behavior of the Mabuchi energy along any degeneration is logarithmic, 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. I also provide necessary and sufficient conditions for the properness of the Mabuchi functional along all degenerations in terms of the Hyperdiscriminant and Chow polytopes.