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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Computation of the topological type of a real Riemann surface
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by C. Kalla and C. Klein PDF
Math. Comp. 83 (2014), 1823-1846 Request permission


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:
  • C. Klein
  • Affiliation: Institut de Mathématiques de Bourgogne, Université de Bourgogne, 9 avenue Alain Savary, 21078 Dijon Cedex, France
  • Email:
  • 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.
  • © Copyright 2014 American Mathematical Society
  • Journal: Math. Comp. 83 (2014), 1823-1846
  • MSC (2010): Primary 14Q05; Secondary 68W30
  • DOI:
  • MathSciNet review: 3194131