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A complex that resolves the ideal of minors having $ n-1$ columns in common

Authors: J. F. Andrade and A. Simis
Journal: Proc. Amer. Math. Soc. 81 (1981), 217-219
MSC: Primary 13D25; Secondary 14M12
MathSciNet review: 593460
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Abstract: Let $ A$ be an $ n \times m$ matrix $ (m \geqslant n)$ with entries in a noetherian ring $ R$, let $ J$ be the ideal of $ R$ generated by the $ n \times n$ minors that are formed with $ n - 1$ fixed columns of $ A$. Necessary and sufficient conditions are given in order that a suitably defined complex be a free resolution of the $ R$-module $ R/J$. The complex is closely related to the complexes of Buchsbaum-Rim [2, §2] and it is perhaps worthwhile mentioning that a special case of the present result was obtained by Buchsbaum-Eisenbud in a different context [1, Theorem 8.1].

References [Enhancements On Off] (What's this?)

  • [1] D. Buchsbaum and D. Eisenbud, Some structure theorems for finite free resolutions, Advances in Math. 12 (1974), 84-139. MR 0340240 (49:4995)
  • [2] -, Remarks on ideals and resolutions, Symposia Mathematica, Vol. 11, Academic Press, London, 1973, pp. 191-204. MR 0337946 (49:2715)
  • [3] J. Eagon and D. Northcott, Ideals defined by matrices and a certain complex associated to them, Proc. Royal Soc. Ser. A 269 (1962), 188-204. MR 0142592 (26:161)

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