On the normal sheaf of determinantal varieties

Let X be a standard determinantal scheme X subset of P-n of codimension c, i.e. a scheme defined by the maximal minors of a t x (t + c - 1) homogeneous polynomial matrix A. In this paper, we study the main features of its normal sheaf N-X. We prove that under some mild restrictions: (1) there exists a line bundle L on X \ Sing (X) such that N-X circle times L is arithmetically Cohen-Macaulay and, even more, it is Ulrich whenever the entries of A are linear forms, (2) N-X is simple (hence, indecomposable) and, finally, (3) N-X is mu-(semi)stable provided the entries of A are linear forms.