Geodesic
Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics
Sean Timothy Paul1
1 Department of Mathematics<br/> University of Wisconsin Madison<br/> 480 Lincoln Drive<br/> Madison, WI 53706-1388
Annals of mathematics, Tome 175 (2012) no. 1, pp. 255-296.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Let $X^n\rightarrow \mathbb{P}^N$ be a smooth, linearly normal algebraic variety. It is shown that the Mabuchi energy of $(X,{\omega_{FS}}|_X)$ 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 $G$.
DOI : 10.4007/annals.2012.175.1.7

Sean Timothy Paul 1

1 Department of Mathematics<br/> University of Wisconsin Madison<br/> 480 Lincoln Drive<br/> Madison, WI 53706-1388 
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Sean Timothy Paul. Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics. Annals of mathematics, Tome 175 (2012) no. 1, pp. 255-296. doi : 10.4007/annals.2012.175.1.7. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.175.1.7/

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