This article is cited in 1 paper

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

I. A. Mednykh<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University, Novosibirsk

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.

UDC: 517.545

Received: 10.05.2011

 English version: Siberian Mathematical Journal, 2012, 53:2, 259–273

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