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 | References | Similar Articles | Additional Information

When is a Gorenstein ideal of grade in a local ring , results of Boffi and Sánchez, and of Kustin and Ulrich show that for each one can construct in a canonical way a finite free complex that is ``approximately" a resolution for the ideal . Kustin and Ulrich also provide a sufficient condition that is acyclic, and a sufficient condition that is a resolution of . 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

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