Remote Access Mathematics of Computation
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $\tau$.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 14Q05, 68W30

Retrieve articles in all journals with MSC (2010): 14Q05, 68W30

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

C. Klein
Affiliation: Institut de Mathématiques de Bourgogne, Université de Bourgogne, 9 avenue Alain Savary, 21078 Dijon Cedex, France

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