Mathematical Research Letters

Volume 22 (2015)

Number 5

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

Pages: 1563 – 1571

DOI: http://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.

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