Quadratic Euler Characteristic of Symmetric Powers of Curves
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929387794857984 |
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| author | Bröring, Lukas F. Viergever, Anna M. |
| author_facet | Bröring, Lukas F. Viergever, Anna M. |
| contents | We compute the quadratic Euler characteristic of the symmetric powers of a smooth, projective curve over any field $k$ that is not of characteristic two, using the Motivic Gauss-Bonnet Theorem of Levine-Raksit. As an application, we show over a field of characteristic zero that the power structure on the Grothendieck-Witt ring introduced by Pajwani-Pál computes the compactly supported $\mathbb{A}^1$-Euler characteristic of symmetric powers for all curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quadratic Euler Characteristic of Symmetric Powers of Curves Bröring, Lukas F. Viergever, Anna M. Algebraic Geometry 14G27, 14N10, 14F42 We compute the quadratic Euler characteristic of the symmetric powers of a smooth, projective curve over any field $k$ that is not of characteristic two, using the Motivic Gauss-Bonnet Theorem of Levine-Raksit. As an application, we show over a field of characteristic zero that the power structure on the Grothendieck-Witt ring introduced by Pajwani-Pál computes the compactly supported $\mathbb{A}^1$-Euler characteristic of symmetric powers for all curves. |
| title | Quadratic Euler Characteristic of Symmetric Powers of Curves |
| topic | Algebraic Geometry 14G27, 14N10, 14F42 |
| url | https://arxiv.org/abs/2404.16378 |