V. Shramchenko
Efficient computation of the branching structure of an algebraic curve.
Thu, 08/11/2011 - 15:01 — SomNambulAuthors: V. Shramchenko, C. Klein, J. Frauendiener
Subjects: Computational Geometry
AbstractAn efficient algorithm for computing the branching structure of a compact
Riemann surface defined via an algebraic curve is presented. Generators of the
fundamental group of the base of the ramified covering punctured at the
discriminant points of the curve are constructed via a minimal spanning tree of
the discriminant points. This leads to paths of minimal length between the
points, which is important for a later stage where these paths are used as
integration contours to compute periods of the surface.Riemann-Hilbert problem for Hurwitz Frobenius manifolds: regular singularities.
Fri, 09/04/2009 - 12:10 — SomNambulAuthors: D. Korotkin, V. Shramchenko
Subjects: Mathematical Physics
AbstractIn this paper we study the Fuchsian Riemann-Hilbert (inverse monodromy)
problem corresponding to Frobenius structures on Hurwitz spaces. We find a
solution to this Riemann-Hilbert problem in terms of integrals of certain
meromorphic differentials over a basis of an appropriate relative homology
space over a Riemann surface, study the corresponding monodromy group and
compute the monodromy matrices explicitly for various special cases.
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