Local and global applications of the minimal model program for co-rank 1 foliations on threefolds
type: Item
instance of: scholarly article
title: Local and global applications of the minimal model program for co-rank 1 foliations on threefolds
DOI: 10.4171/JEMS/1173
author: Calum Spicer
author: Roberto Svaldi
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2022-10-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/1908.05037
review text: Summary: We provide several applications of the minimal model program to the local and global study of co-rank 1 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 log canonical centres, a non-vanishing theorem and some hyperbolicity properties of foliations.
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 37F75
Mathematics Subject Classification ID: 32S65
zbMATH DE Number: 7608246
zbMATH Keywords: foliations
zbMATH Keywords: minimal model program
zbMATH Keywords: singularities
zbMATH Keywords: separatrices
zbMATH Keywords: hyperbolicity
MaRDI profile type: Publication
cites work: On Fano foliations
cites work: Rational Curves on Foliated Varieties
cites work: Q4801049
cites work: Quadratic forms and holomorphic foliations on singular surfaces
cites work: Q3684836
cites work: Reduction of the singularities of codimension one singular foliations in dimension three
cites work: Desingularization of non-dicritical holomorphic foliations and existence of separatrices
cites work: Integral hypersurfaces and holomorphic manifolds
cites work: Invariant surfaces for toric type foliations in dimension three
cites work: Local Brunella's Alternative II. Partial Separatrices
cites work: Local Brunella's Alternative I. RICH Foliations
cites work: MMP for co-rank one foliations on threefolds
cites work: Frobenius theorem for foliations on singular varieties
cites work: Codimension \(1\) foliations with numerically trivial canonical class on singular spaces
cites work: Divisorenklassengruppen quasihomogener Singularitäten.
cites work: Germs of holomorphic vector fields in \(\mathbb{C}^ 3\) without a separatrix
cites work: Differential forms on log canonical spaces
cites work: Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of abelian varieties
cites work: Q4143433
cites work: Pull-back morphisms for reflexive differential forms
cites work: Toroidal embeddings. I
cites work: Q4212603
cites work: Singular foliations with trivial canonical class
cites work: Frobenius avec singularites. I: Codimension un
cites work: Holonomie et intégrales premières
cites work: Diophantine approximations and foliations
cites work: Canonical models of foliations
cites work: Almost étale resolution of foliations
cites work: Kodaira dimension of holomorphic singular foliations
cites work: Effective algebraic integration in bounded genus
cites work: Extending coherent analytic sheaves
cites work: Higher-dimensional foliated Mori theory
cites work: Hyperbolicity for log canonical pairs and the cone theorem
cites work: Finiteness of fundamental groups
description: scientific article; zbMATH DE number 7608246