On properness of K-moduli spaces and optimal degenerations of Fano varieties

Autor:	Blum, Harold, Halpern-Leistner, Daniel, Liu, Yuchen, Xu, Chenyang
Rok vydání:	2020
Předmět:	Mathematics - Algebraic Geometry Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	We establish an algebraic approach to prove the properness of moduli spaces of K-polystable Fano varieties and reduce the problem to a conjecture on destabilizations of K-unstable Fano varieties. Specifically, we prove that if the stability threshold of every K-unstable Fano variety is computed by a divisorial valuation, then such K-moduli spaces are proper. The argument relies on studying certain optimal destabilizing test configurations and constructing a Theta-stratification on the moduli stack of Fano varieties. Comment: v2: to appear in Selecta Math
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2011.01895 Zobrazit plný text záznamu View this record from Arxiv