Explicit Constructions for Genus 3 Jacobians

Jesus Romero-Valencia; Alexis G. Zamora

Explicit Constructions for Genus 3 Jacobians

Algebraic Geometry 2009-04-30 v1

Authors: Jesus Romero-Valencia , Alexis G. Zamora

Abstract

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.

Keywords

hyperelliptic curves abel-jacobi theory jacobian conjecture

Cite

@article{arxiv.0904.4537,
  title  = {Explicit Constructions for Genus 3 Jacobians},
  author = {Jesus Romero-Valencia and Alexis G. Zamora},
  journal= {arXiv preprint arXiv:0904.4537},
  year   = {2009}
}

Comments

12 pages

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