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arXiv · 2503.00926

Principalization on logarithmically foliated orbifolds

Dan Abramovich·André Belotto da Silva·Michael Temkin·Jarosław Włodarczyk
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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.

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Dan Abramovich, André Belotto da Silva, Michael Temkin, Jarosław Włodarczyk. 2025-03-02. Principalization on logarithmically foliated orbifolds. https://arxiv.org/abs/2503.00926

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