MMP for co-rank one foliations on threefolds

2018/08/08 by Cascini, Paolo, Spicer, Calum · 9 citations
#Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.02711

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.

Cited by

• Volumes of foliations birationally bounded by algebraically integrable families
• Explicit bounds on foliated surfaces and the Poincaré problem
• Regular Leaves of Singular Foliations
• Variation of algebraically integrable adjoint foliated structures
• Non-algebraicity of non-abundant foliations and abundance for adjoint foliated structures
• On base point freeness for rank one foliations
• Toric reduction of singularities for Newton nondegenerate p-forms
• MMP for generalized foliated threefolds of rank one
• Sarkisov program for algebraically integrable and threefold foliations

Related

• On the MMP for rank one foliations on threefolds
• MMP for generalized foliated threefolds of rank one
• MMP for algebraically integrable foliations
• Log Canonical Minimal Model Program for corank one foliations on Threefolds
• On base point freeness for rank one foliations