Minimal models, flips and finite generation : a tribute to V.V. SHOKUROV and Y.-T. SIU

2009/04/19 by Caucher Birkar, Mihai Păun, Birkar, Caucher +1 · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0904.2936

openalex publication_date 2009/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we discuss a proof of existence of log minimal models or Mori fibre spaces for klt pairs (X/Z,B) with B big/Z. This then implies existence of klt log flips, finite generation of klt log canonical rings, and most of the other results of Birkar-Cascini-Hacon-McKernan paper.

Citations

• A General Non-Vanishing Theorem and an Analytic Proof of the Finite Generation of the Canonical Ring
• Finite generation of a canonical ring

Cited by

• On existence of log minimal models and weak Zariski decompositions
• Adjoint rings are finitely generated

Related

• Log minimal models according to Shokurov
• Existence of flips and minimal models for 3-folds in char p
• Log canonical pairs with boundaries containing ample divisors
• Minimal model theory for relatively trivial log canonical pairs
• Some remarks on the minimal model program for log canonical pairs