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СЕМИНАРЫ |
Петербургский геометрический семинар им. А. Д. Александрова
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Holomorphic maps of Riemann surfaces and de Franchis theorem А. Д. Медныхab, И. А. Медныхba a Институт математики им. С.Л. Соболева Сибирского отделения Российской академии наук, г. Новосибирск b Новосибирский государственный университет |
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Аннотация: Denote by The classical theorem of de Franchis states that the cardinality of the set 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 is attained when the target Riemann surface is the Bolza curve. Also, we discuss possible generalizations of the de Franchis theorem on high dimensional case as well as on the case of hyperbolic orbifolds. |