Families of Determinantal Schemes
Original version
Kleppe, J.O. & Miro-Roig, R.M. (2011). Families of Determinantal Schemes. Proceedings of the American Mathematical Society, posted on March 17, 2011 (to appear in print) http://dx.doi.org/10.1090/S0002-9939-2011-10802-5Abstract
Given integers a_0 <= a_1 <= ... <= a_{t+c-2} and b_1 <= ... <= b_t, we denote by W(b;a) \subset Hilb^p(P^n) the locus of good determinantal schemes X in P^n 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(P^n).