Vol. 2, 2019

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Numerical computation of endomorphism rings of Jacobians

Nils Bruin, Jeroen Sijsling and Alexandre Zotine

Vol. 2 (2019), No. 1, 155–171
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
curves, Riemann surfaces, period matrices, automorphisms, endomorphisms, isogeny factors
Mathematical Subject Classification 2010
Primary: 14H40, 14H37, 14H55, 14Q05
Supplementary material

Example code for numerical endomorphisms

Milestones
Received: 2 March 2018
Revised: 18 June 2018
Accepted: 10 September 2018
Published: 13 February 2019
Authors
Nils Bruin
Department of Mathematics
Simon Fraser University
Burnaby, BC
Canada
Jeroen Sijsling
Institut für Reine Mathematik
Universität Ulm
Ulm
Germany
Alexandre Zotine
Department of Mathematics
Simon Fraser University
Burnaby, BC
Canada