FROM PICARD GROUPS OF HYPERELLIPTIC CURVES TO CLASS GROUPS OF QUADRATIC FIELDS

Let C be a hyperelliptic curve defined over Q, whose Weierstrass points are defined over extensions of Q of degree at most three, and at least one of them is rational. Generalizing a result of R. Soleng (in the case of elliptic curves), we prove that any line bundle of degree 0 on C which is not torsion can be specialised into ideal classes of imaginary quadratic fields whose order can be made arbitrarily large. This gives a positive answer, for such curves, to a question by Agboola and Pappas.