Numerical computation of endomorphism rings
Number Theory
2019-06-13 v2 Algebraic Geometry
Abstract
We give practical numerical methods to compute the period matrix of a plane algebraic curve (not necessarily smooth). We show how automorphisms and isomorphisms of such curves, as well as the decomposition of their Jacobians up to isogeny, can be calculated heuristically. Particular applications include the determination of (generically) non-Galois morphisms between curves and the identification of Prym varieties.
Keywords
Cite
@article{arxiv.1807.02605,
title = {Numerical computation of endomorphism rings},
author = {Nils Bruin and Jeroen Sijsling and Alexandre Zotine},
journal= {arXiv preprint arXiv:1807.02605},
year = {2019}
}
Comments
16 pages; ancillary computer scripts; accepted for ANTS 2018