Quadratic Euler Characteristic of Geometrically Cyclic Branched Coverings
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909040247832576 |
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| author | Bröring, Louisa F. |
| author_facet | Bröring, Louisa F. |
| contents | For an $n$-fold geometrically cyclic branched covering $Y$ of a smooth, projective scheme $X$ branched at a smooth closed subscheme $Z\subset X$ with $n \in k^\times$, we compute the quadratic Euler characteristic of $Y$ in terms of certain Euler classes on $X$ and $Z$ using the quadratic Riemann-Hurwitz formula of Levine. In certain cases with $n$ odd, we relate the quadratic Euler characteristic of $Y$ to the quadratic Euler characteristics of $X$ and $Z$, obtaining similar formulae to the situation in topology.
As an application, we compute the quadratic Euler characteristic of geometrically cyclic branched double coverings of $\mathbb{P}^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13425 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quadratic Euler Characteristic of Geometrically Cyclic Branched Coverings Bröring, Louisa F. Algebraic Geometry For an $n$-fold geometrically cyclic branched covering $Y$ of a smooth, projective scheme $X$ branched at a smooth closed subscheme $Z\subset X$ with $n \in k^\times$, we compute the quadratic Euler characteristic of $Y$ in terms of certain Euler classes on $X$ and $Z$ using the quadratic Riemann-Hurwitz formula of Levine. In certain cases with $n$ odd, we relate the quadratic Euler characteristic of $Y$ to the quadratic Euler characteristics of $X$ and $Z$, obtaining similar formulae to the situation in topology. As an application, we compute the quadratic Euler characteristic of geometrically cyclic branched double coverings of $\mathbb{P}^2$. |
| title | Quadratic Euler Characteristic of Geometrically Cyclic Branched Coverings |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2605.13425 |