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Hilbert schemes of suitable smooth, projective manifolds of low degree whichare 3-fold scrolls over the Hirzebruch surface F_1 are studied. An irreduciblecomponent of the Hilbert scheme parametrizing such varieties is shown to begenerically smooth of the expected dimension and the general point of such acomponent is described.

Hilbert scheme of some threefold scrolls over the Hirzebruch surface F_1