A note on large automorphism groups of compact Riemann surfaces
| Autor: | Sebastián Reyes-Carocca, Milagros Izquierdo |
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| Rok vydání: | 2018 |
| Předmět: |
Isogeny
Pure mathematics Algebra and Number Theory Group (mathematics) Riemann surface 010102 general mathematics Prime number Riemann surfaces Group actions Jacobian varieties Geometry Automorphism 01 natural sciences Mathematics - Algebraic Geometry symbols.namesake Genus (mathematics) 0103 physical sciences symbols FOS: Mathematics Order (group theory) Geometri 010307 mathematical physics 0101 mathematics Large group Algebraic Geometry (math.AG) Mathematics |
| DOI: | 10.48550/arxiv.1811.08371 |
| Popis: | Belolipetsky and Jones classified those compact Riemann surfaces of genus $g$ admitting a large group of automorphisms of order $\lambda (g-1)$, for each $\lambda >6,$ under the assumption that $g-1$ is a prime number. In this article we study the remaining large cases; namely, we classify Riemann surfaces admitting $5(g-1)$ and $6(g-1)$ automorphisms, with $g-1$ a prime number. As a consequence, we obtain the classification of Riemann surfaces admitting a group of automorphisms of order $3(g-1)$, with $g-1$ a prime number. We also provide isogeny decompositions of their Jacobian varieties. Comment: 12 pages, To appear in Journal of Algebra |
| Databáze: | OpenAIRE |
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