Abstract
We consider the problem of finding an upper bound for the possible torsion of a divisor on a curve of genus 2, when everything is defined over an algebraic number field. Mainly, we show how to write the equation of the Kummer surface of the Jacobian of a curve of genus 2 in terms of the equation of the curve. This allows one to calculate a bound on the torsion which seems better than the bound derived from Riemann-Weil theory. Finally, we discuss briefly a different approach which is valid for all hy — perelliptic curves, at the cost of a considerable increase in complexity.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
