6533b823fe1ef96bd127ec8a

RESEARCH PRODUCT

Efficient computation of the branching structure of an algebraic curve

Jörg FrauendienerJörg FrauendienerVasilisa ShramchenkoChristian Klein

subject

Discrete mathematicsCircular algebraic curveComputational Geometry (cs.CG)FOS: Computer and information sciencesStable curveApplied MathematicsButterfly curve (algebraic)010102 general mathematics010103 numerical & computational mathematics01 natural sciencesModular curveMathematics - Algebraic GeometryComputational Theory and Mathematics14Q05Algebraic surfaceFOS: MathematicsComputer Science - Computational GeometryAlgebraic functionAlgebraic curve0101 mathematicsHyperelliptic curveAlgebraic Geometry (math.AG)AnalysisMathematics

description

An 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. The branching structure of the surface is obtained by analytically continuing the roots of the equation defining the algebraic curve along the constructed generators of the fundamental group.

yearjournalcountryeditionlanguage
2012-01-01
http://arxiv.org/abs/1108.2038