Revêtements hyperelliptiques d-osculateurs et solitons elliptiques de la hiérarchie KdV

Details Revêtements hyperelliptiques d-osculateurs et solitons elliptiques de la hiérarchie KdV Revêtements hyperelliptiques d-osculateurs et solitons elliptiques de la hiérarchie KdV

2009-12-04

arxiv.org/abs/0912.0784v1

Comptes Rendus de l Acad\'emie des Sciences - Series I - Mathematics 345 (2007) 213-218

Mathematics

Algebraic Geometry

Scientific paper

Let $d$ be a positive integer, $\mathbb K$ 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 $KdV$ flow.

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