Explicit Constructions for Genus 3 Jacobians
Jesus Romero-Valencia, Alexis G. Zamora

TL;DR
This paper presents explicit algebraic constructions and algorithms for the Jacobian of genus 3 curves, including affine equations, group law descriptions, and embeddings into Grassmannian varieties.
Contribution
It introduces new explicit equations and algorithms for the Jacobian of genus 3 curves, extending Mumford's ideas for hyperelliptic cases.
Findings
Explicit equations for an affine open subset of the Jacobian.
Algorithms describing the group law on the Jacobian.
A construction embedding the Jacobian into a Grassmannian variety.
Abstract
Given a canonical genus three curve , we construct, emulating Mumford discussion for hyperelliptic curves, a set of equations for an affine open subset of the jacobian . We give explicit algorithms describing the law group in . Finally we introduce a related construction by means of an imbedding of the open set previously described in a Grassmanian variety.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Dynamics and Control of Mechanical Systems · Polynomial and algebraic computation
