An explicit Construction of the Jacobian of a nonsingular curve and its group law

Details An explicit Construction of the Jacobian of a nonsingular curve and its group law An explicit Construction of the Jacobian of a nonsingular curve and its group law

2006-05-06

arxiv.org/abs/math/0605170v1

Mathematics

Algebraic Geometry

Scientific paper

This paper is devoted to constructing an explicit efficient representation for the Jacobian variety of a nonsingular curve of genus greater than 1, and its group law. We describe an algorithm for executing the group law on the Jacobian elements, consisting of several steps. Finally we exhibit two examples. The first example exhibits an explicit formulation for the Jacobian of a well known non singular elliptic curve of genus 1, that is, the Weierstrass curve. The second example introduces an explicit computation of the group law for a non singular curve of genus 3, $C : \omega_2^4 = \omega_1 (\omega_1-\omega_0)(\omega_1-2\omega_0)(\omega_1-3\omega_0)$, where $\omega_0, \omega_1, \omega_2$ are homogeneous coordinates of the projective plane $\mathbb{P}^2$. These examples are highly detailed for the convenience of the reader.

Affiliated with

Also associated with

No associations

Rating

An explicit Construction of the Jacobian of a nonsingular curve and its group law does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An explicit Construction of the Jacobian of a nonsingular curve and its group law, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An explicit Construction of the Jacobian of a nonsingular curve and its group law will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-67045