Open AccessPosted Content
Existence of log canonical modifications and its applications
Osamu Fujino,Kenta Hashizume +1 more
TLDR
The main purpose of as discussed by the authors is to establish some useful partial resolutions of singularities for pairs from the minimal model theoretic viewpoint, and to recover Kawakita's inversion of adjunction on log canonicity in full generality.Abstract:
The main purpose of this paper is to establish some useful partial resolutions of singularities for pairs from the minimal model theoretic viewpoint. We first establish the existence of log canonical modifications of normal pairs under some suitable assumptions. It recovers Kawakita's inversion of adjunction on log canonicity in full generality. We also discuss the existence of semi-log canonical modifications for demi-normal pairs and construct dlt blow-ups with several extra good properties. As applications, we study lengths of extremal rational curves and so on.read more
Citations
More filters
Posted Content
Existence of flips for generalized lc pairs
Christopher D. Hacon,Jihao Liu +1 more
TL;DR: In this article, the existence of flips for NQC generalized lc pairs was proved, and the cone and contraction theorems for generalized Lc pairs were shown to be true.
Posted Content
Adjunction and inversion of adjunction
Osamu Fujino,Kenta Hashizume +1 more
TL;DR: In this article, the authors established adjunction and inversion of adjunction for log canonical centers of arbitrary codimension in full generality, in the sense that they can be invertive.
Posted Content
On inversion of adjunction
Osamu Fujino,Kenta Hashizume +1 more
TL;DR: In this article, the relationship between the inversion of adjunction and Hacon's inversion for log canonical centers of arbitrary codimension was clarified, and the relation between the two was established.
Posted Content
Crepant semi-divisorial log terminal model
TL;DR: In this paper, the existence of a crepant sdlt model for slc pairs whose irreducible components are normal in codimension one is proved. But it is not known whether the model can be applied to the case of non-normal components.
Posted Content
On quasi-log schemes
TL;DR: In this paper, the authors established the basepoint-free theorem of Reid-Fukuda type for quasi-log schemes in full generality, which means that all the results for quasilog schemes claimed in Ambro's paper hold true.
References
More filters
Journal ArticleDOI
Existence of minimal models for varieties of log general type
TL;DR: In this paper, it was shown that pl-flips exist in dimension n − 1, assuming finite generation in dimension N − 1 and assuming that pl flips exist in all dimensions.
Journal ArticleDOI
Threefolds and deformations of surface singularities
TL;DR: In this paper, the authors studied the study of surface singularities using recent advances in 3D geometry and proved the existence of a minimal resolution of singularities for a given set of surfaces.
Journal ArticleDOI
Fundamental Theorems for the Log Minimal Model Program
TL;DR: In this article, the authors proved the cone theorem and the contraction theorem for pairs (X;B), where X is a normal variety and B is an effective R-Divisor on X such that KX + B is R-Cartier.
Journal ArticleDOI
Log canonical singularities are Du Bois
János Kollár,Sándor J. Kovács +1 more
TL;DR: In this article, it was shown that log canonical singularities are Du Bois, as conjectured in [Kol92, 1.13] and [1.10].
Journal ArticleDOI
Inversion of adjunction on log canonicity
TL;DR: In this paper, the authors prove inversion of adjunction on log canonicity, and prove that adjunction is invertible on log canonicity, but not on log-canonicity.