Families of determinantal schemes.

Jan O. Kleppe and Rosa M. Mir'o-Roig

Given integers a₀, a₁,..., a_t+c-2 and b₁,...,b_t we denote by W(b;a) of Hilb^p(Pⁿ) the locus of good determinantal schemes X of Pⁿ of codimension c defined by the maximal minors of a t x (t+c-1) homogeneous matrix with entries homogeneous polynomials of degree a_j-b_i. The goal of this short note is to extend and complete the results given by the authors in [10] and determine under weakened numerical assumptions the dimension of W(b;a), as well as whether the closure of W(b;a) is a generically smooth irreducible component of the Hilbert scheme Hilb^p(Pⁿ).