Explicit Constructions for Genus 3 Jacobians

Details Explicit Constructions for Genus 3 Jacobians Explicit Constructions for Genus 3 Jacobians

2009-04-29

arxiv.org/abs/0904.4537v1

Mathematics

Algebraic Geometry

12 pages

Scientific paper

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.

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