Computing period matrices and the Abel-Jacobi map of superelliptic curves
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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.References
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Additional Information
- Pascal Molin
- Affiliation: IMJ-PRG & Université Paris 7, 8 place Aurélie Nemours, 75013 Paris, France
- MR Author ID: 884381
- Email: molin@math.univ-paris-diderot.fr
- Christian Neurohr
- Affiliation: Carl von Ossietzky Universität Oldenburg, Institut für Mathematik, 26129 Oldenburg, Germany
- Email: neurohrchristian@googlemail.com
- Received by editor(s): October 6, 2017
- Received by editor(s) in revised form: December 8, 2017
- Published electronically: May 30, 2018
- Additional Notes: The first author was partially supported by Partenariat Hubert Curien under grant 35487PL
The second author was partially supported by DAAD under grant 57212102. - © Copyright 2018 American Mathematical Society
- Journal: Math. Comp. 88 (2019), 847-888
- MSC (2010): Primary 11Y16, 11Y35; Secondary 14Q05, 65D30, 11G30
- DOI: https://doi.org/10.1090/mcom/3351
- MathSciNet review: 3882287