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arXiv · 2601.12558

Remarks on the second Chern class of a foliation

Alan Muniz
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Abstract

We bound the second Chern class of the tangent sheaf of a codimension-one foliation. Equivalently, we bound the degree of the pure codimension-two part of the singular scheme. In particular, for a degree-$d$ foliation on the projective space, the codimension-two part of its singular scheme must have degree at least $d+1$. Moreover, equality holds only for rational foliations of type $(1,d+1)$. These bounds involve counting an invariant related to first-order unfoldings of 2-dimensional foliated singularities.

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Alan Muniz. 2026-01-18. Remarks on the second Chern class of a foliation. https://arxiv.org/abs/2601.12558

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