MMP for co-rank one foliations on threefolds
Paolo Cascini,Calum Spicer +1 more
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In this paper, the existence of flips, special termination, base point free theorem and minimal models for foliated pairs of co-rank one on a projective projective is proved.Abstract:
We prove existence of flips, special termination, the base point free theorem and, in the case of log general type, the existence of minimal models for F-dlt foliated pairs of co-rank one on a $${\mathbb {Q}}$$
-factorial projective threefold. As applications, we show the existence of F-dlt modifications and F-terminalisations for foliated pairs and we show that foliations with canonical or F-dlt singularities admit non-dicritical singularities. Finally, we show abundance in the case of numerically trivial foliated pairs.read more
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Local and global applications of the Minimal Model Program for co-rank one foliations on threefolds
Calum Spicer,Roberto Svaldi +1 more
TL;DR: In this article, the authors provide several applications of the minimal model program to the local and global study of co-rank one foliations on three-folds, including termination of flips, connectedness theorem on lc centres, a non-vanshing theorem and some hyperbolicity properties of foliations.
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Del Pezzo foliations with log canonical singularities
TL;DR: In this paper, the authors classify del Pezzo foliations of rank at least 3 on projective manifolds and with log canonical singularities in the sense of McQuillan.
On semi-ampleness of the moduli part
Stefano Filipazzi,Calum Spicer +1 more
TL;DR: In this paper , the authors discuss a conjecture of Shokurov on the semi-amplenes of the moduli part of a general π-bration and show that it is true.
Frobenius integrability of certain $p$-forms on singular spaces
TL;DR: In this paper , Demailly proved that on a smooth compact K-ahler manifold, the distribution of a holomorphic p-form with values in an anti-pseudo-ective line bundle is always integrable.
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Codimension One Foliations with Numerically Trivial Canonical Class on Singular Spaces II
Stéphane Druel,Wenhao Ou +1 more
TL;DR: In this article, the structure of codimension one foliations with canonical singularities and numerically trivial canonical class on varieties with klt singularities is given, based on recent works of Spicer, Cascini-Spicer and Spicer-Svaldi.
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Éléments de géométrie algébrique
TL;DR: In this paper, 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.
Book
Introduction to Commutative Algebra
TL;DR: It is shown here how the Noetherian Rings and Dedekind Domains can be transformed into rings and Modules of Fractions using the following structures:
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 Article
Éléments de géométrie algébrique : III. Étude cohomologique des faisceaux cohérents, Seconde partie
TL;DR: In this paper, the authors implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.html).
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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.