About the group law for the Jacobi variety of a hyperelliptic curve

Details About the group law for the Jacobi variety of a hyperelliptic curve About the group law for the Jacobi variety of a hyperelliptic curve

2005-09-27

arxiv.org/abs/math/0509638v1

Beitr. Algebra Geom. 46, No.1, 125-130 (2005)

Mathematics

Algebraic Geometry

5 pages

Scientific paper

We generalize the group law of curves of degree three by chords and tangents
to the Jacobi variety of a hyperelliptic curve. In the case of genus 2 we
accomplish the construction by a cubic parabola. We derive explicit rational
formulas for the addition on a dense set in the Jacobian.

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