Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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
MathSciNet review: 1432144
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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

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