Mathematics – Differential Geometry
Scientific paper
2008-11-16
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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