On the normal sheaf of determinantal varieties
| Autor: | Kleppe, Jan O., Miró-Roig, Rosa M. |
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| Rok vydání: | 2014 |
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| Zdroj: | J. Reine Angew. Math. (online 18.06.2014) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1515/crelle-2014-0041 |
| Popis: | 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. Comment: 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 |
| Databáze: | arXiv |
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