Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics
Differential Geometry
2010-09-03 v3 Algebraic Geometry
Abstract
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 .
Cite
@article{arxiv.0811.2548,
title = {Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics},
author = {Sean Timothy Paul},
journal= {arXiv preprint arXiv:0811.2548},
year = {2010}
}
Comments
39 pages. Typos corrected. Theorem F added (page 4) as well as a new section (section 4) which makes the paper self contained