Equations for the Jacobian of a hyperelliptic curve

van Wamelen, Paul

doi:10.1090/S0002-9947-98-02056-X

Equations for the Jacobian of a hyperelliptic curve
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Trans. Amer. Math. Soc. 350 (1998), 3083-3106 Request permission

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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