Kreuzer, Martin and Migliore, Juan C. and Peterson, Chris and Nagel, Uwe (2000) Determinantal schemes and Buchsbaum-Rim sheaves. JOURNAL OF PURE AND APPLIED ALGEBRA, 150 (2). pp. 155-174. ISSN 0022-4049
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Let phi be a generically surjective morphism between direct sums of line bundles on P-n and assume that the degeneracy locus, X, of phi has the expected codimension. We call B-phi = ker phi a (first) Buchsbaum-Rim sheaf and we call X a standard determinantal scheme. Viewing phi as a matrix (after choosing bases), we say that X is good if one can delete a generalized row from phi and have the maximal miners of the resulting submatrix define a scheme of the expected codimension. In this paper we give several characterizations of good determinantal schemes. In particular, it is shown that being a good determinantal scheme of codimension r + 1 is equivalent to being the zero-locus of a regular section of the dual of a first Buchsbaum-Rim sheaf of rank r + 1. It is also equivalent to being standard determinantal and locally a complete intersection outside a subscheme Y subset of X of codimension r + 2. Furthermore, for any good determinantal subscheme X of codimension r + 1 there is a good determinantal subscheme S codimension r such that X sits in S in a nice way. This leads to several generalizations of a theorem of Kreuzer. For example, we show that for a zeroscheme X in P-3, being good determinantal is equivalent to the existence of an arithmetically Cohen-Macaulay curve S, which is a local complete intersection, such that X is a subcanonical Cartier divisor on S. (C) 2000 Elsevier Science B.V. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CURVES; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 Apr 2022 12:42 |
| Last Modified: | 05 Apr 2022 12:42 |
| URI: | https://pred.uni-regensburg.de/id/eprint/42395 |
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