Mathematical Research Letters

Volume 22 (2015)

Number 5

A quadratic point on the Jacobian of the universal genus four curve

Pages: 1563 – 1571

DOI: https://dx.doi.org/10.4310/MRL.2015.v22.n5.a13

Author

Hang Xue (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Abstract

In this paper, we construct a point on the Jacobian of a non-hyperelliptic genus four curve which is defined over a quadratic extension of the base field. We then show that this point generates the Mordell–Weil group of the Jacobian of the universal genus four curve.

Accepted 24 October 2014

Published 13 April 2016