Monodromy of the Prym map and semicanonical pencils in genus 6
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913862636273664 |
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| author | Lahoz, Martí Naranjo, Juan Carlos Rojas, Andrés Spelta, Irene |
| author_facet | Lahoz, Martí Naranjo, Juan Carlos Rojas, Andrés Spelta, Irene |
| contents | The Prym map $\mathcal{P}_6$ in genus 6 is dominant and generically finite of degree 27. When restricted to the divisor of curves with an odd semicanonical pencil $\mathcal{T}_6^o$, it is still generically finite, but of degree strictly smaller. In this paper, we prove that $\mathcal{P}_6$ restricted to $\mathcal{T}_6^o$ is birational and that the monodromy group over the image of $\mathcal{T}_6^o$ is the Weyl group $WD_5$. Thus, there are two other irreducible divisors in the moduli space of Prym curves $\mathcal{R}_6$ and the degree of $\mathcal{P}_6$ restricted to them is 10 and 16. Moreover, we study the geometry of the divisor where $\mathcal{P}_6$ has degree 10. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13443 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monodromy of the Prym map and semicanonical pencils in genus 6 Lahoz, Martí Naranjo, Juan Carlos Rojas, Andrés Spelta, Irene Algebraic Geometry The Prym map $\mathcal{P}_6$ in genus 6 is dominant and generically finite of degree 27. When restricted to the divisor of curves with an odd semicanonical pencil $\mathcal{T}_6^o$, it is still generically finite, but of degree strictly smaller. In this paper, we prove that $\mathcal{P}_6$ restricted to $\mathcal{T}_6^o$ is birational and that the monodromy group over the image of $\mathcal{T}_6^o$ is the Weyl group $WD_5$. Thus, there are two other irreducible divisors in the moduli space of Prym curves $\mathcal{R}_6$ and the degree of $\mathcal{P}_6$ restricted to them is 10 and 16. Moreover, we study the geometry of the divisor where $\mathcal{P}_6$ has degree 10. |
| title | Monodromy of the Prym map and semicanonical pencils in genus 6 |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2407.13443 |