A complex that resolves the ideal of minors having $n-1$ columns in common
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- by J. F. Andrade and A. Simis PDF
- Proc. Amer. Math. Soc. 81 (1981), 217-219 Request permission
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, ยง2] 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
- David A. Buchsbaum and David Eisenbud, Some structure theorems for finite free resolutions, Advances in Math. 12 (1974), 84โ139. MR 340240, DOI 10.1016/S0001-8708(74)80019-8
- David A. Buchsbaum and David Eisenbud, Remarks on ideals and resolutions, Symposia Mathematica, Vol. XI (Convegno di Algebra Commutativa, INDAM, Rome, 1971) Academic Press, London, 1973, pp.ย 193โ204. MR 0337946
- J. A. Eagon and D. G. Northcott, Ideals defined by matrices and a certain complex associated with them, Proc. Roy. Soc. London Ser. A 269 (1962), 188โ204. MR 142592, DOI 10.1098/rspa.1962.0170
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 217-219
- MSC: Primary 13D25; Secondary 14M12
- DOI: https://doi.org/10.1090/S0002-9939-1981-0593460-5
- MathSciNet review: 593460