6533b7dcfe1ef96bd1272a7d
RESEARCH PRODUCT
Computation of the topological type of a real Riemann surface
Caroline Kalla Christian Kleinsubject
Computational Geometry (cs.CG)FOS: Computer and information sciencesreal Riemann surface[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]homology basis[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Algebraic Geometryreal algebraic curveholomorphic differentialsFOS: MathematicsComputer Science - Computational Geometryreal ovals[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Algebraic Geometry (math.AG)description
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 $\tau$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-04-22 |