Hurwitz moduli varieties parameterizing Galois covers of an algebraic curve
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866929339712405504 |
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| author | Kanev, Vassil |
| author_facet | Kanev, Vassil |
| contents | Given a smooth, projective curve $Y$, a finite group $G$ and a positive integer $n$ we study smooth, proper families $X\to Y\times S\to S$ of Galois covers of $Y$ with Galois group isomorphic to $G$ branched in $n$ points, parameterized by algebraic varieties $S$. When $G$ is with trivial center we prove that the Hurwitz space $H^G_n(Y)$ is a fine moduli variety for this moduli problem and construct explicitly the universal family. For arbitrary $G$ we prove that $H^G_n(Y)$ is a coarse moduli variety. For families of pointed Galois covers of $(Y,y_0)$ we prove that the Hurwitz space $H^G_n(Y,y_0)$ is a fine moduli variety, and construct explicitly the universal family, for arbitrary group $G$. We use classical tools of algebraic topology and of complex algebraic geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_06020 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hurwitz moduli varieties parameterizing Galois covers of an algebraic curve Kanev, Vassil Algebraic Geometry 14H30 (Primary) 14H10, 14D22 (Secondary) Given a smooth, projective curve $Y$, a finite group $G$ and a positive integer $n$ we study smooth, proper families $X\to Y\times S\to S$ of Galois covers of $Y$ with Galois group isomorphic to $G$ branched in $n$ points, parameterized by algebraic varieties $S$. When $G$ is with trivial center we prove that the Hurwitz space $H^G_n(Y)$ is a fine moduli variety for this moduli problem and construct explicitly the universal family. For arbitrary $G$ we prove that $H^G_n(Y)$ is a coarse moduli variety. For families of pointed Galois covers of $(Y,y_0)$ we prove that the Hurwitz space $H^G_n(Y,y_0)$ is a fine moduli variety, and construct explicitly the universal family, for arbitrary group $G$. We use classical tools of algebraic topology and of complex algebraic geometry. |
| title | Hurwitz moduli varieties parameterizing Galois covers of an algebraic curve |
| topic | Algebraic Geometry 14H30 (Primary) 14H10, 14D22 (Secondary) |
| url | https://arxiv.org/abs/2205.06020 |