Log canonical 3-fold complements

2019/09/22 by Stefano Filipazzi, Filipazzi, Stefano, Joaquí­n Moraga +3
Mathematics · #14E30 (Primary) #14F18 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1909.10098

openalex publication_date 2019/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We expand the theory of log canonical 3-fold complements. We prove that if X→ T is a 3-dimensional contraction of log Calabi-Yau type, then we can find B≥ 0 on X for which (X,B) is log canonical and n(K_X+B)∼_T 0, where n is an uniform natural number. This means that every 3-fold of log Calabi-Yau type can be turned into a log Calabi-Yau pair in an effective way.

Citations

• ACC for minimal log discrepancies of exceptional singularities
• Some Results about the Index Conjecture for log Calabi-Yau Pairs
• Q-complements on log surfaces

Related

• The LMMP for log canonical 3-folds in char p
• Complements on log canonical Fano varieties
• A Torelli Theorem for log Calabi--Yau threefolds
• Birational complexity of log Calabi-Yau 3-folds
• Finite generation of the log canonical ring for 3-folds in char p