Quadratic Segre indices
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914282216620032 |
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| author | Espreafico, Felipe McKean, Stephen Pauli, Sabrina |
| author_facet | Espreafico, Felipe McKean, Stephen Pauli, Sabrina |
| contents | We prove that the local Euler class of a line on a degree $2n-1$ hypersurface in projective $n+1$ space is given by a product of indices of Segre involutions. Segre involutions and their associated indices were first defined by Finashin and Kharlamov over the reals. Our result is valid over any perfect field of characteristic not 2 and gives an infinite family of problems in enriched enumerative geometry with a shared geometric interpretation for the local type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01547 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quadratic Segre indices Espreafico, Felipe McKean, Stephen Pauli, Sabrina Algebraic Geometry 14N15, 14G27 We prove that the local Euler class of a line on a degree $2n-1$ hypersurface in projective $n+1$ space is given by a product of indices of Segre involutions. Segre involutions and their associated indices were first defined by Finashin and Kharlamov over the reals. Our result is valid over any perfect field of characteristic not 2 and gives an infinite family of problems in enriched enumerative geometry with a shared geometric interpretation for the local type. |
| title | Quadratic Segre indices |
| topic | Algebraic Geometry 14N15, 14G27 |
| url | https://arxiv.org/abs/2506.01547 |