Resolution of $1$-foliations singularities on surfaces and threefolds

Abstract

We consider resolution of singularities for $1$-foliations on varieties of dimension at most three in positive characteristic. We prove that such singularities can be completely resolved if we allow tame regular Deligne--Mumford stacks as underlying spaces. If one restricts to underlying varieties, we show that $1$-foliations singularities can be simplified into multiplicative ones.

arXiv commentv2: 40 pages, comments welcome. The discussion of foliations on DM stacks has been improved; the resolution on surfaces has been upgraded to a functorial statement; an appendix on Cossart's work on normal forms has been added