Toric foliation

Intro

toric foliation

toric foliated pair md

Main results

foliation mmp:

toric foliated mmp md

foliated pair mmp:

fmmp for toric foliated pair md

cone theorem:

cone for foliated toric md

fibration:

fibration for pair md

Why toric foliation?

Because we can

singularity

We need **foliated** log smooth resolution for foliated pairs.

defn fLS md

mld for fLS md

defn fdlt md

high dimensional algebraic integrable foliation

toroidal morphism md

equi-dimensional model md

foliated log smooth md

defn fLSR md

has foliated log resulution md

fLS and lc md

toroidal to lc md

Foliation on toric

Preliminaries

sheaves

equ qcoh sheaf and families md

defn filtration of vec sp md

c1 of equ reflexive md

defn c1 md

local generator

local generators of toric foliation md

Properties

invariant divisor md

tangent curve md

tangent subvar md

F-invariant divisor md

non-dicritical singularity md

Singularity

description

dagger condition md

fdlt and fls foliated toric md

log canonical etc foliated toric md

non-dicritical on smooth toric md

relations

singularity of foliated toric pair md

under MMP

pull back of foliation md

Cone theorem

tangent extremal ray

decompose curve into eff and tangent class md

fibration

Q-factorial not pair:

fibration of foliation md

pair an non-Q-factorial:

lemma: toric projective bundles md