Computing period matrices and the Abel-Jacobi map of superelliptic curves - Archive ouverte HAL Access content directly
Journal Articles Mathematics of Computation Year : 2019

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

(1, 2, 3) , (4)
1
2
3
4

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.
Fichier principal
Vignette du fichier
periods.pdf (729.38 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

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⟩
215 View
280 Download

Share

Gmail Facebook Twitter LinkedIn More