2011/05/02 by Caucher Birkar, Birkar, Caucher
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #math.AG
paper · pdf · doi:10.48550/arxiv.1105.0441
19 pages. A typo in Theorem 1.2 is corrected that was caused by some last minute changes
openalex publication_date 2011/05/02 · arxiv created 2011/05/04 · arxiv updated 2011/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study certain modules over the algebra of a Cartier divisor on a scheme. Using these modules, we present an inductive method for studying finite generation properties of algebras and modules. In the context of the minimal model program, we show that finite generation of log canonical algebras and modules is equivalent to the minimal model and abundance conjectures.