MonographDOI
Singularities of the minimal model program
János Kollár,Sándor J. Kovács +1 more
- Iss: 200
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In this paper, the authors present a survey of Canonical and log canonical singularities and their application in the context of finite equivalence relations, including semi-log-canonical pairs and the Du Bois property.Abstract:
Preface Introduction 1. Preliminaries 2. Canonical and log canonical singularities 3. Examples 4. Adjunction and residues 5. Semi-log-canonical pairs 6. Du Bois property 7. Log centers and depth 8. Survey of further results and applications 9. Finite equivalence relations 10. Appendices References Index.read more
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Journal ArticleDOI
Canonical bases for cluster algebras
TL;DR: In this paper, it was shown that the ring of regular functions on a natural class of affine log Calabi-Yau varieties (those with maximal boundary) has a canonical vector space basis parameterized by the integral tropical points of the mirror.
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Canonical bases for cluster algebras
TL;DR: In this article, it was shown that the ring of regular functions on a natural class of affine log Calabi-Yau varieties (those with maximal boundary) has a canonical vector space basis parameterized by the integral tropical points of the mirror.
Journal ArticleDOI
K-semistability is equivariant volume minimization
TL;DR: In this article, it was shown that ordV is the unique minimizer among all C∗-invariant quasimonomial valuations on the cone associated to any positive Cartier multiple of −KV.
Journal ArticleDOI
On the three dimensional minimal model program in positive characteristic
Christopher D. Hacon,Chenyang Xu +1 more
TL;DR: In this article, the existence of minimal models for any projective projective terminal variety with pseudo-effective canonical divisor (K_X) is proved. But the model is not optimal.
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Uniform K-stability, Duistermaat-Heckman measures and singularities of pairs
TL;DR: In this paper, a formalism inspired from non-archimedean geometry to study K-stability was proposed, where the Donaldson-Futaki invariant is interpreted as the non-Archimediean version of the Mabuchi functional, up to an explicit error term.