MMP for co-rank one foliations on threefolds

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.

89 pages. Revision based on comments from the referee. Inventiones Math. (to appear)

References in corpus (3)

• 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

Cited by in corpus (4)

• Codimension one foliations with numerically trivial canonical class on singular spaces
• Effective generation for foliated surfaces: results and applications
• Codimension one foliations with trivial canonical class on singular spaces II
• Towards classification of codimension 1 foliations on threefolds of general type