Symmetric and Alternating Groups As Monodromy Groups of Riemann Surfaces, Volume 1 Generic Covers and Covers with Many Branch Points - with an Appendix by R. Guralnick and R. Stafford |
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| Author:
| Guralnick, Robert
Shareshian, John |
| Series title: | Memoirs of the American Mathematical Society Ser. |
| ISBN: | 978-0-8218-3992-8 |
| Publication Date: | Jul 2007 |
| Publisher: | American Mathematical Society
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| Book Format: | Paperback |
| List Price: | USD $73.00USD $73.00 |
Book Description:
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Considers indecomposable degree $n$ covers of Riemann surfaces with monodromy group an alternating or symmetric group of degree $d$. The authors show that if the cover has five or more branch points then the genus grows rapidly with $n$ unless either $d = n$ or the curves have genus zero, there are precisely five branch points and $n =d(d-1)/2$.
Considers indecomposable degree $n$ covers of Riemann surfaces with monodromy group an alternating or symmetric group of degree $d$. The authors show that if the cover has five or more branch points then the genus grows rapidly with $n$ unless either $d = n$ or the curves have genus zero, there are precisely five branch points and $n =d(d-1)/2$.