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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Acyclicity criteria for complexes associated with an alternating map


Author: Alexandre B. Tchernev
Journal: Proc. Amer. Math. Soc. 129 (2001), 2861-2869
MSC (2000): Primary 13D02, 13D05, 13D25, 14M12
Published electronically: March 29, 2001
MathSciNet review: 1840088
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Abstract:

When $I$ is a Gorenstein ideal of grade $3$ in a local ring $R$, results of Boffi and Sánchez, and of Kustin and Ulrich show that for each $t\ge 1$one can construct in a canonical way a finite free complex $\mathcal{D}^{t}$ that is ``approximately" a resolution for the ideal $I^{t}$. Kustin and Ulrich also provide a sufficient condition that $\mathcal{D}^{t}$ is acyclic, and a sufficient condition that $\mathcal{D}^{t}$ is a resolution of $I^{t}$. We complete these two acyclicity criteria by showing that the corresponding sufficient conditions are also necessary.


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Additional Information

Alexandre B. Tchernev
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Address at time of publication: Department of Mathematics and Statistics, University at Albany, SUNY, Albany, New York 12222
Email: tchernev@math.albany.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05935-4
PII: S 0002-9939(01)05935-4
Keywords: Alternating matrix, finite free resolution, Gorenstein ideal, Pfaffian
Received by editor(s): December 19, 1998
Received by editor(s) in revised form: February 29, 2000
Published electronically: March 29, 2001
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2001 American Mathematical Society