On the number of real curves associated to a complex algebraic curve
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- by Emilio Bujalance, Grzegorz Gromadski and David Singerman PDF
- Proc. Amer. Math. Soc. 120 (1994), 507-513 Request permission
Abstract:
Using non-Euclidean crystallographic groups we give a short proof of a theorem of Natanzon that a complex algebraic curve of genus $g \geqslant 2$ has at most $2(\sqrt g + 1)$ real forms. We also describe the topological type of the real curves in the case when this bound is attained. This leads us to solve the following question: how many bordered Riemann surfaces can have a given compact Riemann surface of genus $g$ as complex double?References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 507-513
- MSC: Primary 20H10; Secondary 20H15, 30F50
- DOI: https://doi.org/10.1090/S0002-9939-1994-1165047-6
- MathSciNet review: 1165047