Algebraic uniqueness of K\'{a}hler-Ricci flow limits and optimal degenerations of Fano varieties

Autor:	Han, Jiyuan, Li, Chi
Rok vydání:	2020
Předmět:	Mathematics - Algebraic Geometry Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	We prove that for any $\mathbb{Q}$-Fano variety $X$, the special $\mathbb{R}$-test configuration that minimizes the $H$-functional is unique and has a K-semistable $\mathbb{Q}$-Fano central fibre $(W, \xi)$. Moreover there is a unique K-polystable degeneration of $(W, \xi)$. As an application, we confirm the conjecture of Chen-Sun-Wang about the algebraic-uniqueness for K\"{a}hler-Ricci flow limits on Fano manifolds, which implies that the Gromov-Hausdorff limit of the flow does not depend on the choice of initial K\"{a}hler metrics. The results are achieved by studying algebraic optimal degeneration problems via new functionals of real valuations, which are analogous to the minimization problem for normalized volumes. Comment: 48 pages. Comments Welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2009.01010 Zobrazit plný text záznamu View this record from Arxiv