Existence of log canonical closures

2011/05/05 by Christopher D. Hacon, Chenyang Xu, Hacon, Christopher D. +1 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1105.1169

openalex publication_date 2011/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f:X→ U be a projective morphism of normal varieties and (X,Δ) a dlt pair. We prove that if there is an open set U⁰⊂ U, such that (X,Δ)×_U U⁰ has a good minimal model over U⁰ and the images of all the non-klt centers intersect U⁰, then (X,Δ) has a good minimal model over U. As consequences we show the existence of log canonical compactifications for open log canonical pairs, and the fact that the moduli functor of stable schemes satisfies the valuative criterion for properness.

Citations

• Quotients by finite equivalence relations
• Introduction to the log minimal model program for log canonical pairs
• A semiampleness criterion
• Log pluricanonical representations and abundance conjecture
• Base point free theorems--saturation, b-divisors, and canonical bundle formula--
• Existence of log canonical flips and a special LMMP

Cited by

• On quasi-Albanese morphisms for log canonical Calabi-Yau pairs
• Stein degree on non-Fano type fibrations
• Effective termination of general type MMPs in dimension at most five

Related

• Log canonical pairs with boundaries containing ample divisors
• Varieties fibred over abelian varieties with fibres of log general type
• The Dual Complex of a semi-log canonical Surface
• On the non-vanishing conjecture and existence of log minimal models
• Introduction to the log minimal model program for log canonical pairs