On existence of log minimal models and weak Zariski decompositions

DOI10.1007/s00208-011-0756-yzbMath1255.14016arXiv0907.5182OpenAlexW2118337711MaRDI QIDQ453415

Caucher Birkar

Publication date: 27 September 2012

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.5182

zbMATH Keywords

minimal modelLC pairsweak Zariski decomposition

Mathematics Subject Classification ID

Minimal model program (Mori theory, extremal rays) (14E30) Divisors, linear systems, invertible sheaves (14C20)

Related Items (15)

On the existence of minimal models for log canonical pairs ⋮ Higher dimensional elliptic fibrations and Zariski decompositions ⋮ Polarized pairs, log minimal models, and Zariski decompositions ⋮ The diminished base locus is not always closed ⋮ Weak Zariski decompositions and log terminal models for generalized pairs ⋮ Pseudo-effective cones of projective bundles and weak Zariski decomposition ⋮ Log canonical algebras and modules ⋮ Birational Geometry of Projective Varieties and Directed Graphs ⋮ On the existence of a weak Zariski decomposition on projectivized vector bundles ⋮ On partially ample adjoint divisors ⋮ Generalised pairs in birational geometry ⋮ On generalised abundance. II ⋮ Special MMP for log canonical generalised pairs (with an appendix joint with Xiaowei Jiang) ⋮ Unnamed Item ⋮ Potential density of projective varieties having an int-amplified endomorphism

Cites Work

• Zariski decomposition and canonical rings of elliptic threefolds
• Log minimal models according to Shokurov
• Semi-ampleness of the numerically effective part of Zariski decomposition
• On Zariski problem
• Termination of 4-fold canonical flips
• Zariski-decomposition and abundance
• Letters of a bi-rationalist. VII: Ordered termination
• The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface
• On existence of log minimal models II
• Existence of minimal models for varieties of log general type
• The Iitaka conjecture C_n,m in dimension six
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