Remarks on the second Chern class of a foliation
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917209519947776 |
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| author | Muniz, Alan |
| author_facet | Muniz, Alan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12558 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Remarks on the second Chern class of a foliation Muniz, Alan Algebraic Geometry Complex Variables 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. |
| title | Remarks on the second Chern class of a foliation |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2601.12558 |