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

2005/09/27 by Frank Leitenberger · 1 citation
Mathematics · #math.AG #msc:14H40

paper · pdf

published as Beitr. Algebra Geom. 46, No.1, 125-130 (2005) · 5 pages

arxiv created 2005/09/27 · arxiv updated 2009/12/01

Abstract

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.

Cited by

• On the generalised Kummer fourfold of the Jacobian of a genus two curve

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