Hilbert scheme of some threefold scrolls over the Hirzebruch surface $¥mathbb F$<sub>1</sub>

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  • Besana Gian Mario
    College of Computing and Digital Media, DePaul University
  • Fania Maria Lucia
    Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Università degli Studi di L'Aquila
  • Flamini Flaminio
    Dipartimento di Matematica, Università degli Studi di Roma Tor Vergata, Viale della Ricerca Scientifica

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  • Hilbert scheme of some threefold scrolls over the Hirzebruch surface F₁
  • Hilbert scheme of some threefold scrolls over the Hirzebruch surface ${\mathbb F}_1$

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Abstract

Hilbert schemes of suitable smooth, projective manifolds of low degree which are 3-fold scrolls over the Hirzebruch surface $¥mathbb F$1 are studied. An irreducible component of the Hilbert scheme parametrizing such varieties is shown to be generically smooth of the expected dimension and the general point of such a component is described.

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