Boundedness of moduli of varieties of general type

2014/12/03 by Christopher D. Hacon, Hacon, Christopher, James McKernan +3 · 8 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1412.1186

openalex publication_date 2014/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the family of semi log canonical pairs with ample log canonical class and with fixed volume is bounded.

Citations

• Pluricanonical systems of projective varieties of general type

Cited by

• Volumes of foliations birationally bounded by algebraically integrable families
• Non-algebraicity of non-abundant foliations and abundance for adjoint foliated structures
• Stein degree on log Calabi-Yau fibrations
• Non-extendable MMPs
• On volumes and the generic invariance of Fano type varieties
• Effective positivity of Hodge bundles and applications
• Boundedness of complements for fibered Fano threefolds in positive characteristic
• Projectivity of the moduli space of stable log-varieties and\n subadditvity of log-Kodaira dimension

Related

• Boundedness of varieties of log general type
• Moduli of varieties of general type
• Logarithmic abelian varieties, Part VII: Moduli
• Semi log resolution
• Log canonical singularities and complete moduli of stable pairs