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arXiv · 2203.11094

On the Resolutions of Non-Dicritical Foliations

Philip J. Carter
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Abstract

We introduce the jet schemes of a holomorphic foliation, and thereby prove an alternate characterisation of simple singularities of codimension-$1$ foliations, independent of any normal form. This leads to an equivalent condition for the existence of a desingularisation in the non-dicritical case. We then prove that such a desingularisation always exists, at least on the level of germs.

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Philip J. Carter. 2022-03-21. On the Resolutions of Non-Dicritical Foliations. https://arxiv.org/abs/2203.11094

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