Explicit Constructions for Genus 3 Jacobians

Given a canonical genus three curve \(X=\{F=0\}\), we construct, emulating Mumford discussion for hyperelliptic curves, a set of equations for an affine open subset of the jacobian \(JX\). We give explicit algorithms describing the law group in \(JX\). Finally we introduce a related construction by...

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Bibliographic Details
Published in:arXiv.org 2009-04
Main Authors: Romero-Valencia, Jesus, Zamora, Alexis G
Format: Article
Language:English
Subjects:
Algorithms
Jacobians
Online Access:Get full text
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Summary:Given a canonical genus three curve \(X=\{F=0\}\), we construct, emulating Mumford discussion for hyperelliptic curves, a set of equations for an affine open subset of the jacobian \(JX\). We give explicit algorithms describing the law group in \(JX\). Finally we introduce a related construction by means of an imbedding of the open set previously described in a Grassmanian variety.
ISSN:2331-8422