Ampleness of the CM line bundle on the moduli space of canonically polarized varieties

2015/03/30 by Zsolt Patakfalvi, Chenyang Xu, Patakfalvi, Zsolt +1 · 1 citation
Mathematics · #14E30 #14J10 #14J15 #32Q05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1503.08668

openalex publication_date 2015/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the CM line bundle is ample on the proper moduli space which parametrizes KSBA stable varieties.

Citations

• CM Stability and the Generalized Futaki Invariant I
• Semipositivity theorems for moduli problems

Cited by

• Non-algebraicity of non-abundant foliations and abundance for adjoint foliated structures

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• The Moduli Space of smooth Ample Hypersurfaces in Abelian Varieties