The class of the Prym-Brill-Noether divisor
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918331272921088 |
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| author | Bud, Andrei |
| author_facet | Bud, Andrei |
| contents | For $r\geq 3$ and $g= \frac{r(r+1)}{2}$, we study the Prym-Brill-Noether variety $V^r(C,η)$ associated to Prym curves $[C,η]$. The locus $\mathcal{R}_g^r$ in $\mathcal{R}_g$ parametrizing Prym curves $(C, η)$ with nonempty $V^r(C,η)$ is a divisor. We compute some key coefficients of the class $[\overline{\mathcal{R}}_g^r]$ in $\mathrm{Pic}_\mathbb{Q}(\overline{\mathcal{R}}_g)$. Furthermore, we examine a strongly Brill-Noether divisor in $\overline{\mathcal{M}}_{g-1,2}$: we show its irreducibility and compute some of its coefficients in $\mathrm{Pic}_\mathbb{Q}(\overline{\mathcal{M}}_{g-1,2})$. As a consequence of our results, the moduli space $\mathcal{R}_{14,2}$ is of general type. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_13034 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The class of the Prym-Brill-Noether divisor Bud, Andrei Algebraic Geometry For $r\geq 3$ and $g= \frac{r(r+1)}{2}$, we study the Prym-Brill-Noether variety $V^r(C,η)$ associated to Prym curves $[C,η]$. The locus $\mathcal{R}_g^r$ in $\mathcal{R}_g$ parametrizing Prym curves $(C, η)$ with nonempty $V^r(C,η)$ is a divisor. We compute some key coefficients of the class $[\overline{\mathcal{R}}_g^r]$ in $\mathrm{Pic}_\mathbb{Q}(\overline{\mathcal{R}}_g)$. Furthermore, we examine a strongly Brill-Noether divisor in $\overline{\mathcal{M}}_{g-1,2}$: we show its irreducibility and compute some of its coefficients in $\mathrm{Pic}_\mathbb{Q}(\overline{\mathcal{M}}_{g-1,2})$. As a consequence of our results, the moduli space $\mathcal{R}_{14,2}$ is of general type. |
| title | The class of the Prym-Brill-Noether divisor |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2409.13034 |