Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics | Annals of Mathematics

Abstract Let Xn→ℙN be a smooth, linearly normal algebraic variety. It is shown that the Mabuchi energy of (X,ωFS|X) restricted to the Bergman metrics is completely determined by the X-hyperdiscriminant of format (n−1) and the Chow form of X. As a corollary it is shown that the Mabuchi energy is bounded from below for all degenerations in G if and only if the hyperdiscriminant polytope dominates the Chow polytope for all maximal algebraic tori H of G.

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数学年刊(Annals of Mathematics)

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