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A Note on the Multiplicity of Cohen-Macaulay Algebras with Pure Resolutions

Published online by Cambridge University Press:  20 November 2018

Craig Huneke  and
Matthew Miller
Craig Huneke
Affiliation:
Purdue University, W. Lafayette, Indiana
Matthew Miller
Affiliation:
University of Tennessee, Knoxville, Tennessee
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Let R = k[X1, …, Xn] with k a field, and let I ⊂ R be a homogeneous ideal. The algebra R/I is said to have a pure resolution if its homogeneous minimal resolution has the form

Some of the known examples of pure resolutions include the coordinate rings of: the tangent cone of a minimally elliptic singularity or a rational surface singularity [15], a variety defined by generic maximal Pfaffians [2], a variety defined by maximal minors of a generic matrix [3], a variety defined by the submaximal minors of a generic square matrix [6], and certain of the Segre-Veronese varieties [1].

If I is in addition Cohen-Macaulay, then Herzog and Kühl have shown that the betti numbers bi are completely determined by the twists di.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 6 , 01 December 1985 , pp. 1149 - 1162
Copyright
Copyright © Canadian Mathematical Society 1985

References

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