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Journal Articles Mathematics of Computation Year : 2019

Computing period matrices and the Abel-Jacobi map of superelliptic curves

Abstract

We present an algorithm for the computation of period matrices and the Abel-Jacobi map of complex superelliptic curves given by an equation y m = f (x). It relies on rigorous numerical integration of differentials between Weierstrass points, which is done using Gauss method if the curve is hyperelliptic (m = 2) or the Double-Exponential method. The algorithm is implemented and makes it possible to reach thousands of digits accuracy even on large genus curves.
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Dates and versions

hal-02416012 , version 1 (17-12-2019)

Identifiers

  • HAL Id : hal-02416012 , version 1

Cite

Pascal Molin, Christian Neurohr. Computing period matrices and the Abel-Jacobi map of superelliptic curves. Mathematics of Computation, 2019. ⟨hal-02416012⟩
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