Abstract
Let d be a positive integer, K an algebraically closed field of characteristic 0 and X an elliptic curve defined over K . We study the hyperelliptic curves equipped with a projection over X, such that the natural image of X in the Jacobian of the curve osculates to order d to the embedding of the curve, at a Weierstrass point. We construct ( d − 1 )-dimensional families of such curves, of arbitrary big genus g, obtaining, in particular, ( g + d − 1 ) -dimensional families of solutions of the KdV hierarchy, doubly periodic with respect to the d-th variable. To cite this article: A. Treibich, C. R. Acad. Sci. Paris, Ser. I 345 (2007).
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