A Hurwitz divisor on the Moduli of Prym curves
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866909111092772864 |
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| author | Bud, Andrei |
| author_facet | Bud, Andrei |
| contents | For genus $g=2i\geq4$ and the length $g-1$ partition $μ= (4,2,\ldots,2,-2,\ldots,-2)$ of 0, we compute the first coefficients of the class of $\overline{D}(μ)$ in $\mathrm{Pic}_\mathbb{Q}(\overline{\mathcal{R}}_g)$, where $D(μ)$ is the divisor consisting of pairs $[C,η]\in \mathcal{R}_g$ with $η\cong \mathcal{O}_C(2x_1+x_2+\cdots + x_{i-1}-x_i-\cdots-x_{2i-1})$ for some points $x_1,\ldots, x_{2i-1}$ on $C$. We further provide several enumerative results that will be used for this computation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_14947 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A Hurwitz divisor on the Moduli of Prym curves Bud, Andrei Algebraic Geometry For genus $g=2i\geq4$ and the length $g-1$ partition $μ= (4,2,\ldots,2,-2,\ldots,-2)$ of 0, we compute the first coefficients of the class of $\overline{D}(μ)$ in $\mathrm{Pic}_\mathbb{Q}(\overline{\mathcal{R}}_g)$, where $D(μ)$ is the divisor consisting of pairs $[C,η]\in \mathcal{R}_g$ with $η\cong \mathcal{O}_C(2x_1+x_2+\cdots + x_{i-1}-x_i-\cdots-x_{2i-1})$ for some points $x_1,\ldots, x_{2i-1}$ on $C$. We further provide several enumerative results that will be used for this computation. |
| title | A Hurwitz divisor on the Moduli of Prym curves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2104.14947 |