Computation of the topological type of a real Riemann surface

Details Computation of the topological type of a real Riemann surface Computation of the topological type of a real Riemann surface

2012-04-21

arxiv.org/abs/1204.4826v1

Mathematics

Algebraic Geometry

23 pages, 5 figures

Scientific paper

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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