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Transactions of the American Mathematical Society
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 | 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

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02056-X
PII: S 0002-9947(98)02056-X
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