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

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arxiv 2405.05735 v2 pith:7HAP3CKW submitted 2024-05-09 math.AG

Quentin Posva This is my paper · ORCID
classification math.AG
keywords singularitiesfoliationsresolutionunderlyingvarietiesallowcharacteristiccompletely
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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.

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  1. Pathological MMP singularities as $\alpha_p$-quotients

    math.AG 2025-01 conditional novelty 8.0 of 10

    For every positive characteristic, the author constructs non-S3 terminal singularities of dimension p+1 and stable families with klt, Cohen-Macaulay, F-injective general fibers but non-S2 special fibers.

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