Principalization on logarithmically foliated orbifolds
Algebraic Geometry
2025-03-24 v2
Abstract
In characteristic zero, we construct principalization of ideals on smooth orbifolds endowed with a normal crossings divisor and a foliation. We then illustrate how the method can be used in the general study of foliations via two applications. First, we provide a resolution of singularities of Darboux totally integrable foliations in arbitrary dimensions -- including rational and meromorphic Darboux foliations. Second, we show how to transform a generically transverse section into a transverse section.
Keywords
Cite
@article{arxiv.2503.00926,
title = {Principalization on logarithmically foliated orbifolds},
author = {Dan Abramovich and André Belotto da Silva and Michael Temkin and Jarosław Włodarczyk},
journal= {arXiv preprint arXiv:2503.00926},
year = {2025}
}
Comments
We have introduced the notion of a thick class of foliations. We have also established a criterion for reducing the singularities of the pullback of a foliation in a thick class C to another foliation within the same class