On the number of real curves associated to a complex algebraic curve

Authors:
Emilio Bujalance, Grzegorz Gromadski and David Singerman

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

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Abstract: Using non-Euclidean crystallographic groups we give a short proof of a theorem of Natanzon that a complex algebraic curve of genus has at most 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 as complex double?

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DOI:
https://doi.org/10.1090/S0002-9939-1994-1165047-6

Article copyright:
© Copyright 1994
American Mathematical Society