Computation of the topological type of a real Riemann surface

Kalla, C.; Klein, C.

doi:10.1090/S0025-5718-2014-02817-2

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

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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