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metadata.dc.type: | Artigo de Periódico |
Title: | On ideals of minors fixing a submatrix |
Other Titles: | Journal of Algebra |
Authors: | Andrade, J. F. Simis, A. |
metadata.dc.creator: | Andrade, J. F. Simis, A. |
Abstract: | Let & be a n x m matrix with entries in a noetherian ring R and let A’ be the submatrix of JY consisting of the first r columns (r < n - 1). Consider the ideal J,(A) of n x n minors of J! involving the columns of J/Z’. We obtain the primary decomposition and the homological dimension of J,(d) in the generic case. The proofs rely heavily on the methods and the theory of weak d-sequences and straightening laws. As a byproduct we obtain exact conditions under which Jr(d) is generated by a d-sequence and also a complete picture of the blowing-up algebras of J,(d) in that case. The latter proofs rely on recent methods developed by several authors such as those of sliding-depth, approximation complexes, Cohen-Macaulay residual intersections. To close the discussion we construct a free resolution of J,(d) when m=n+ 1 (the case r =n- 1 had been treated before by the present authors). A side curiosity herein obtained is an example of a nonperfect radical 3-generated ideal of codimension 2 whose associated graded ring is a Cohen-Macaulay reduced ring that is not Gorenstein. Examples of this sort do not seem to abound. |
Publisher: | Journal of Algebra |
URI: | http://www.repositorio.ufba.br/ri/handle/ri/8369 |
Issue Date: | 1986 |
Appears in Collections: | Artigo Publicado em Periódico (IME) |
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