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arXiv · 1403.7383

On the normal sheaf of determinantal varieties

Jan O. Kleppe·Rosa M. Miró-Roig
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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 \mu-(semi)stable provided the entries of A are linear forms.

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Jan O. Kleppe, Rosa M. Miró-Roig. 2014-03-28. On the normal sheaf of determinantal varieties. https://doi.org/10.1515/crelle-2014-0041

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