The dimension of the Hilbert scheme of special threefolds

Research paper by GianMario Besana, Maria Lucia Fania

Indexed on: 06 Dec '04Published on: 06 Dec '04Published in: Mathematics - Algebraic Geometry


The Hilbert scheme of projective 3-folds of codimension 3 or more that are linear scrolls over the projective plane or over a smooth quadric surface or that are quadric or cubic fibrations over the projective line is studied. All known such threefolds of degree from 7 to 11 are shown to correspond to smooth points of an irreducible component of their Hilbert scheme, whose dimension is computed. A relationship with the locus of good determinantal subschemes is investigated