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Vanishing theorems for threefolds in characteristic $p>5$.
Fabio Bernasconi,János Kollár +1 more
TLDR
In this article, the authors prove Grauert-Riemenschneider-type vanishing theorems for excellent dlt three-folds pairs whose closed points have perfect residue fields of positive characteristic $p>5.Abstract:
We prove Grauert-Riemenschneider-type vanishing theorems for excellent dlt threefolds pairs whose closed points have perfect residue fields of positive characteristic $p>5$. Then we discuss applications to dlt singularities and to Mori fiber spaces of threefolds.read more
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Globally +-regular varieties and the minimal model program for threefolds in mixed characteristic
Bhargav Bhatt,Linquan Ma,Zsolt Patakfalvi,Karl Schwede,Kevin Tucker,Joe Waldron,Jakub Witaszek +6 more
TL;DR: In this paper, the Minimal Model Program for arithmetic three-folds whose residue characteristics are greater than five was established, and the theory of global $F$-regularity was generalized to mixed characteristic.
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Relative MMP without Q-factoriality
TL;DR: In this paper, the minimal model program for varieties that are not Q-factorial is considered and the main applications are to log terminal singularities, removing the earlier Qfactoriality assumption from several theorems of Hacon--Witaszek and de~Fernex--Kollar--Xu.
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Relative vanishing theorems for $\mathbf{Q}$-schemes
TL;DR: In this article, the authors prove the relative Grauert-Riemenschneider vanishing, Kawamata-Viehweg vanishing, and Kollar injectivity theorems for locally quasi-excellent ℓ-algebras.
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Relative mmp without $ \mathbb{Q} $-factoriality
TL;DR: The main applications are to log terminal singularities, removing the earlier Q -factoriality assumption from several theorems of Hacon-Witaszek and de Fernex-Kollar-Xu.
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Gluing theory for slc surfaces and threefolds in positive characteristic
Quentin Posva,Quentin Posva +1 more
TL;DR: In this paper, the authors develop a gluing theory in the sense of Kollar for slc surfaces and three-folds in positive characteristic, and apply it to the topology of lc centers on slc threefolds, and to the projectivity of the moduli space of stable surfaces in characteristic p>5.
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Journal ArticleDOI
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.
MonographDOI
Singularities of the minimal model program
János Kollár,Sándor J. Kovács +1 more
TL;DR: 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.
Birational Geometry of Algebraic Varieties
TL;DR: In this paper, the authors define the following basic birational invariants for algebraic surfaces: Vt->V. By using this, they define a non-singular model by Hironaka; this implies that there exist a nonsingular variety V1 and a proper birational map.
Journal ArticleDOI
Rational singularities with applications to algebraic surfaces and unique factorization
Joseph Lipman,Joseph Lipman +1 more
TL;DR: In this article, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.