On the normal sheaf of determinantal varieties

Let be a standard determinantal scheme of codimension , i.e. a scheme defined by the maximal minors of a homogeneous polynomial matrix . In this paper, we study the main features of its normal sheaf . We prove that under some mild restrictions: (1) there exists a line bundle on such that is arithmetically Cohen–Macaulay and, even more, it is Ulrich whenever the entries of are linear forms, (2) is simple (hence, indecomposable) and, finally, (3) is μ-(semi)stable provided the entries of are linear forms.