On the normal sheaf of determinantal varieties

Abstract

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

This version makes a correction to Proposition 3.9 of previous versions on the arXiv, as well as to the published version in Crelle's journal, see Remark 3.18 for details

References in corpus (1)

• Deformations of modules of maximal grade and the Hilbert scheme at determinantal schemes

Cited by in corpus (5)

• Ulrich bundles on ruled surfaces
• The representation type of determinantal varieties
• Deformation and Unobstructedness of Determinantal Schemes
• Families of artinian and low dimensional determinantal rings
• Schur powers of the cokernel of a graded morphism