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Sibirskii Matematicheskii Zhurnal, 2012, Volume 53, Number 2, Pages 325–344 (Mi smj2309)  
This article is cited in 1 scientific paper (total in 1 paper)

On the sharp upper bound for the number of holomorphic mappings of Riemann surfaces of low genus

I. A. Mednykhab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Novosibirsk
Full-text PDF (401 kB) Citations (1)
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Abstract: We obtain an upper bound for the number of holomorphic mappings of a genus 3 Riemann surface onto a genus 2 Riemann surface in a series of cases. In particular, we establish that the number of holomorphic mappings of an arbitrary genus 3 Riemann surface onto an arbitrary genus 2 Riemann surface is at most 48. We show that this estimate is sharp and find pairs of Riemann surfaces for which it is attained.
Keywords: de Franchis theorem, holomorphic mapping, Riemann surface, orbifold, automorphism.
Received: 10.05.2011
English version:
Siberian Mathematical Journal, 2012, Volume 53, Issue 2, Pages 259–273
DOI: https://doi.org/10.1134/S0037446612020097
Bibliographic databases:
Document Type: Article
UDC: 517.545
Language: Russian
Citation: I. A. Mednykh, “On the sharp upper bound for the number of holomorphic mappings of Riemann surfaces of low genus”, Sibirsk. Mat. Zh., 53:2 (2012), 325–344; Siberian Math. J., 53:2 (2012), 259–273
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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