Equations for the Jacobian of a hyperelliptic curve

Author:
Paul van Wamelen

Journal:
Trans. Amer. Math. Soc. **350** (1998), 3083-3106

MSC (1991):
Primary 14H40; Secondary 14H42

DOI:
https://doi.org/10.1090/S0002-9947-98-02056-X

MathSciNet review:
1432144

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Abstract | References | Similar Articles | Additional Information

Abstract: We give an explicit embedding of the Jacobian of a hyperelliptic curve, $y^2 = f(x)$, into projective space such that the image is isomorphic to the Jacobian over the splitting field of $f$. The embedding is a modification of the usual embedding by theta functions with half integer characteristics.

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Additional Information

**Paul van Wamelen**

Affiliation:
Department of Mathematics, University of California, San Diego, San Diego, California 92093

Address at time of publication:
Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803-4918

Email:
wamelen@math.lsu.edu

Keywords:
Jacobian,
hyperelliptic curve,
theta function,
theta constant,
Thomae’s identity

Received by editor(s):
December 5, 1995

Article copyright:
© Copyright 1998
American Mathematical Society