Hilbert schemes of some threefold scrolls over F_e

Abstract

Hilbert schemes of suitable smooth, projective 3-fold scrolls over the Hirzebruch surface F_e, with e > 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. This article generalizes the study of Hilbert schemes done in arXiv:1110.5464 for e=1.

25 pages; revised version after referees' comments; to appear in Advances in Geometry; this article deals with the case of scrolls over F_e, e>1, and thus generalizes the study of Hilbert schemes done in arXiv:1110.5464 for e=1

References in corpus (1)

• Deformations of modules of maximal grade and the Hilbert scheme at determinantal schemes

Cited by in corpus (1)

• On families of rank-2 uniform bundles on Hirzebruch surfaces and Hilbert schemes of their scrolls