On some components of Hilbert schemes of curves

Let I_{d,g,R} be the union of irreducible components of the Hilbert scheme whose general points parametrize smooth, irreducible, curves of degree d, genus g, which are non--degenerate in the projective space P^R. Under some numerical assumptions on d, g and R, we construct irreducible components of I_{d,g,R} other than the so-called distinguished component}, dominating the moduli space Mg of smooth genus--g curves, which are generically smooth and turn out to be of dimension higher than the expected one. The general point of any such a component corresponds to a curve X⊂P^R which is a suitable ramified m--cover of an irrational curve Y⊂P^{R−1}, m⩾2, lying in a surface cone over Y. The paper extends some of the results in previous papers of Y. Choi, H. Iliev, S. Kim (cf. [12,13] in Bibliography).