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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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https://hal.inria.fr/hal-02416012
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Submitted on : Tuesday, December 17, 2019 - 2:46:54 PM
Last modification on : Thursday, February 3, 2022 - 11:18:42 AM
Long-term archiving on: : Wednesday, March 18, 2020 - 5:51:18 PM

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  • HAL Id : hal-02416012, version 1

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

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