2019/07/02 by Chenyang Xu, Xu, Chenyang · 5 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1907.01114
openalex publication_date 2019/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a version of Jonsson-Mustaţǎ's Conjecture, which says for any graded sequence of ideals, there exists a quasi-monomial valuation computing its log canonical threshold. As a corollary, we confirm Chi Li's conjecture that a minimizer of the normalized volume function is always quasi-monomial. Applying our techniques to a family of klt singularities, we show that the volume of klt singularities is a constructible function. As a corollary, we prove that in a family of klt log Fano pairs, the K-semistable ones form a Zariski open set. Together with [Jia17], we conclude that all K-semistable klt Fano varieties with a fixed dimension and volume are parametrized by an Artin stack of finite type, which then admits a separated good moduli space by [BX18, ABHLX19], whose geometric points parametrize K-polystable klt Fano varieties.