Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics

Details Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics

2008-11-16

arxiv.org/abs/0811.2548v3

Mathematics

Differential Geometry

39 pages. Typos corrected. Theorem F added (page 4) as well as a new section (section 4) which makes the paper self contained

Scientific paper

Let X be a smooth, linearly normal algebraic variety. It is shown that the Mabuchi energy of 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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