Local and global applications of the Minimal Model Program for co-rank one foliations on threefolds

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.

55 pages; new version taking into account referee comments, to appear in JEMS

References in corpus (5)

• Higher dimensional foliated Mori theory
• Codimension one foliations with numerically trivial canonical class on singular spaces
• Codimension one foliations with trivial canonical class on singular spaces II
• On connectedness of non-klt loci of singularities of pairs
• On the Iitaka Conjecture $C_{n,m}$ for Kähler Fibre Spaces

Cited by in corpus (5)

• On the connectedness principle and dual complexes for generalized pairs
• On global ACC for foliated threefolds
• Uniform rational polytopes of foliated threefolds and the global ACC
• Complements, index theorem, and minimal log discrepancies of foliated surface singularities
• On The Log Sarkisov Program For Foliations On Projective 3-Folds