The Mathematical Institute, University of Oxford, Eprints Archive

The group law on the jacobian of a curve of genus 2

Flynn, E. V. (1993) The group law on the jacobian of a curve of genus 2. Journal für die reine und angewandte Mathematik, 439 . pp. 45-69. ISSN 0075-4102

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Abstract

An explicit description is given of the group law on the Jacobian of a curve C of genus 2. The Kummer surface provides a useful intermediary stage; bilinear forms relating to the Kummer surface imply that the global group law may be given projectively by biquadratic forms defined over the same ring as the coefficients of C. It is not assumed that C has a rational Weierstrass point, and the theory presented applies over an arbitrary ground field.

Item Type:Article
Uncontrolled Keywords:Group law; Jacobian; Kummer surface.
Subjects:A - C > Algebraic geometry
H - N > Number theory
Research Groups:Number Theory Group
ID Code:271
Deposited By:E. Victor Flynn
Deposited On:12 Jul 2006
Last Modified:20 Jul 2009 14:19

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