Low-genus primitive monodromy groups with a nonunique minimal normal subgroup
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909921036992512 |
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| author | Gerhardt, Spencer McKemmie, Eilidh Neftin, Danny |
| author_facet | Gerhardt, Spencer McKemmie, Eilidh Neftin, Danny |
| contents | Let $X$ be a Riemann surface, and let $f:X\to\mathbb{P}^1_\mathbb{C}$ be an indecomposable (branched) covering of genus $g$ and degree $n$ whose monodromy group has more than one minimal normal subgroup. Closing a gap in the literature, we show that there is only one such covering when $g\leq 1$. Moreover, for arbitrary $g$, there are no such coverings with $n\gg_g 0$ sufficiently large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low-genus primitive monodromy groups with a nonunique minimal normal subgroup Gerhardt, Spencer McKemmie, Eilidh Neftin, Danny Group Theory 20B15, 58K10 Let $X$ be a Riemann surface, and let $f:X\to\mathbb{P}^1_\mathbb{C}$ be an indecomposable (branched) covering of genus $g$ and degree $n$ whose monodromy group has more than one minimal normal subgroup. Closing a gap in the literature, we show that there is only one such covering when $g\leq 1$. Moreover, for arbitrary $g$, there are no such coverings with $n\gg_g 0$ sufficiently large. |
| title | Low-genus primitive monodromy groups with a nonunique minimal normal subgroup |
| topic | Group Theory 20B15, 58K10 |
| url | https://arxiv.org/abs/2501.15538 |