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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
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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.Abstract:
We provide several applications of the minimal model program to the local and global study of co-rank one foliations on threefolds. Locally, we prove a singular variant of Malgrange's theorem, a classification of terminal foliation singularities and the existence of separatrices for log canonical singularities. Globally, we prove termination of flips, a connectedness theorem on lc centres, a non-vanshing theorem and some hyperbolicity properties of foliations.read more
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On the connectedness principle and dual complexes for generalized pairs
Stefano Filipazzi,Roberto Svaldi +1 more
TL;DR: In this paper, the Shokurov-Kollar connectedness conjecture was extended to generalized log Calabi-Yau pairs and generalized it to the dual complex of generalized pairs.
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MMP for co-rank one foliations on threefolds.
Paolo Cascini,Calum Spicer +1 more
TL;DR: 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 Q$-factorial projective was proved.
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Hyperbolicity for log canonical pairs and the cone theorem
TL;DR: In this paper, it was shown that under the condition that there is no non-constant map from the affine line with values in the open strata of the stratification induced by the non-klt locus of a non-canonical pair, the Cone Theorem is ample.
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Codimension one foliations with 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.
Journal ArticleDOI
On the MMP for rank one foliations on threefolds
Paolo Cascini,Calum Spicer +1 more
TL;DR: In this article, the existence of flips and the base point free theorem for log canonical foliated pairs of rank one on a Q-factorial projective klt was proved.
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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.
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.