Search results for "Hyperelliptic curve"

showing 4 items of 4 documents

Efficient computation of the branching structure of an algebraic curve

2012

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 gro…

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
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A direct method to find solutions of some type of coupled Korteweg-de Vries equations using hyperelliptic functions of genus two

2008

Abstract We suggest how one can obtain exact solutions of some type of coupled Korteweg–de Vries equations by means of hyperelliptic functions of genus two.

PhysicsPure mathematicsPartial differential equationDirect methodMathematics::Analysis of PDEsGeneral Physics and AstronomyType (model theory)Nonlinear systemMathematics::Algebraic GeometryNonlinear Sciences::Exactly Solvable and Integrable SystemsGenus (mathematics)Nonlinear Sciences::Pattern Formation and SolitonsHyperelliptic curveComputer Science::Databases
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The Euler characteristics of $mathcal H_g,n$

2007

In this short note, we compute the orbifold and the ordinary Euler characteristic of Hg,n, the moduli space of pointed hyper- elliptic curves. As a by-product, we obtain an identity involving hypergeometric functions.

euler characteristic hyperelliptic curveSettore MAT/03 - Geometria
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Automorphisms of hyperelliptic GAG-codes

2009

Abstract We determine the n –automorphism group of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such group is, up to isomorphism, a subgroup of the automorphism group of the underlying function field.

Abelian varietyDiscrete mathematicsautomorphismsGroup (mathematics)Applied Mathematicsgeneralized algebraic geometry codes.Outer automorphism groupReductive groupAutomorphismTheoretical Computer ScienceCombinatoricsMathematics::Group Theorygeometric Goppa codeAlgebraic groupDiscrete Mathematics and Combinatoricsalgebraic function fieldsSettore MAT/03 - GeometriaIsomorphismfinite fieldsGeometric Goppa codesfinite fieldalgebraic function fieldHyperelliptic curvegeneralized algebraic-geometry codesMathematicsDiscrete Mathematics
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