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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computation of the topological type of a real Riemann surface


Authors: C. Kalla and C. Klein
Journal: Math. Comp. 83 (2014), 1823-1846
MSC (2010): Primary 14Q05; Secondary 68W30
Published electronically: March 13, 2014
MathSciNet review: 3194131
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Abstract: We present an algorithm for the computation of the topological type of a real compact Riemann surface associated to an algebraic curve, i.e., its genus and the properties of the set of fixed points of the anti-holomorphic involution $ \tau $, namely, the number of its connected components, and whether this set divides the surface into one or two connected components. This is achieved by transforming an arbitrary canonical homology basis to a homology basis where the $ \mathcal {A}$-cycles are invariant under the anti-holomorphic involution $ \tau $.


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Additional Information

C. Kalla
Affiliation: Centre de recherches mathématiques Université de Montréal, Case postale 6128, Montréal H3C 3J7, Canada
Address at time of publication: MAPMO, Université d’Orléans, Rue de Chartres, B.P. 6759, 45007 Orléans Cedex 2, France
Email: kalla@crm.umontreal.ca

C. Klein
Affiliation: Institut de Mathématiques de Bourgogne, Université de Bourgogne, 9 avenue Alain Savary, 21078 Dijon Cedex, France
Email: Christian.Klein@u-bourgogne.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-2014-02817-2
PII: S 0025-5718(2014)02817-2
Received by editor(s): April 22, 2012
Received by editor(s) in revised form: December 31, 2012
Published electronically: March 13, 2014
Additional Notes: The authors thank V. Shramchenko for useful discussions and hints. This work was supported in part by the project FroM-PDE funded by the European Research Council through the Advanced Investigator Grant Scheme, and the ANR via the program ANR-09-BLAN-0117-01.
Article copyright: © Copyright 2014 American Mathematical Society