Inversion of adjunction on log canonicity
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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.Abstract:
We prove inversion of adjunction on log canonicity.read more
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Invariance of Plurigenera and boundedness for Generalized Pairs
Stefano Filipazzi,Roberto Svaldi +1 more
TL;DR: In this paper, the authors survey some recent developments in birational geometry concerning the boundedness of algebraic varieties and delineate a strategy to extend some of these results to the case of generalized pairs, first introduced by Birkar and Zhang, when the associated log canonical divisor is ample, and the volume is fixed.
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The dualizing sheaf on first-order deformations of toric surface singularities
Klaus Altmann,János Kollár +1 more
TL;DR: In this paper, the authors explicitly describe infintesimal deformations of cyclic quotient singularities that satisfy one of the deformation conditions introduced by Wahl, Koll\'ar-Shepherd-Barron and Viehweg.
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Theory of non-lc ideal sheaves -basic properties-
TL;DR: The notion of non-lc ideal sheaves was introduced in this article, which is an analogue of the notion of multiplier ideal heaves and has been shown to have the restriction theorem.
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The Angehrn-Siu Type Effective Freeness For Quasi-Log Canonical Pairs
TL;DR: In this article, the Angehrn-Siu Type effective freeness and effective point separation for quasi-log canonical pairs were shown to hold for semidefinite canonical pairs.
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Rationally connected non-Fano type varieties
TL;DR: In this paper, the relation between the classes of rationally connected varieties and varieties of Fano type was studied, and it is known that these classes are birationally equivalent in dimension 2.
References
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Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: II
Book
Birational Geometry of Algebraic Varieties
János Kollár,Shigefumi Mori +1 more
TL;DR: In this paper, the authors introduce the minimal model program and the canonical class of rational curves, and present the singularities of the model program, as well as three dimensional flops.
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