Introduction to the log minimal model program for log canonical pairs

By O. Fujino. 2009

102 citations recorded by the source corpus.

We describe the foundation of the log minimal model program for log canonical pairs according to Ambro's idea. We generalize Koll\'ar's vanishing and torsion-free theorems for embedded simple normal crossing pairs. Then we prove the cone and contraction theorems for quasi-log varieties, especially, for log canonical pairs.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/48c17b0ee406798f77f1b733078b9bc117c135a0

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In Computational Theory and Mathematics

1. F. Catanese
2. O. Fujino
3. Ingrid Bauer
4. Shin-ichi Matsumura
5. C. Birkar
6. Y. Odaka
7. Christopher D. Hacon

In Geometry and Topology

1. Ingrid Bauer
2. F. Catanese
3. Shin-ichi Matsumura
4. O. Fujino
5. Christopher D. Hacon
6. Matteo Penegini
7. C. Birkar
8. Fritz Grunewald

Citations in the corpus

• An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities (2013, background): “of several complex variables. Therefore, according to the context and objectives, there are many contributions to such kind of injectivity theorems (for example, see [Amb12], [Eno90], [EP08], [EV92], [Fuj09], [Fuj13], [Ohs04], [Tak97], and so on). In his paper [Eno90], Enoki gave the following injec”
• A TRANSCENDENTAL APPROACH TO KOLL AR'S INJECTIVITY THEOREM II (2007, background): “We note that the arguments in [11], [12], [14], [15], and [16] are geometric.”
• Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces (2009, methodology): “For the proof, which depends on the mixed Hodge theory, we recommend the reader to see [ F6 , Chapter 2]. It is because [A, Section 3] seems to be inaccessible.”