On the semiampleness of the positive part of CKM Zariski decompositions

Abstract

We study graded rings associated to big divisors on LC pairs whose difference with the log-canonical divisor is nef. For divisors that are positive enough at the LC centers of the pair, we prove the finite generation of such rings if the pair is DLT or the dimension is low, given that a Zariski decomposition exists.

v4: exposition and organization of the paper improved. To appear in "Math. Proc. Camb. Phil.Soc."

References in corpus (5)

• Introduction to the log minimal model program for log canonical pairs
• Termination of (many) 4-dimensional log flips
• Resolution of Singularities -- Seattle Lecture
• Adjoint rings are finitely generated
• Uniruledness of stable base loci of adjoint linear systems with and without Mori Theory

Cited by in corpus (3)

• Log canonical pairs with good augmented base loci
• On log minimal models and Zariski decompositions II
• Note on quasi-numerically positive log canonical divisors