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Holomorphic mappings between compact Riemann surfaces
Published online by Cambridge University Press: 02 February 2009
Abstract
There are only finitely many non-constant holomorphic mappings between two fixed compact Riemann surfaces of genus greater than 1. This result goes under the name of the de Franchis theorem. Having seen that the set of such holomorphic mappings is finite, we naturally want to obtain a bound on its cardinality. It has been known for some time that there exist various bounds depending only on the genera of the surfaces. Here we obtain ‘better’ bounds of the above type, using arguments based on the rigidity of holomorphic mappings and the hyperbolic geometry of surfaces.
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- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 1 , February 2009 , pp. 109 - 126
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- Copyright © Edinburgh Mathematical Society 2009
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