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On multigraded resolutions

Published online by Cambridge University Press:  24 October 2008

Winfried Bruns  and
Jürgen Herzog
Winfried Bruns
Affiliation:
Universität Osnabrück, Standort Vechta. D-49364 Vechta, Germany
Jürgen Herzog
Affiliation:
Universität Essen, FB Mathematik und Informatik, D-45117 Essen, Germany
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Extract

This paper was initiated by a question of Eisenbud who asked whether the entries of the matrices in a minimal free resolution of a monomial ideal (which, after a suitable choice of bases, are monomials) divide the least common multiple of the generators of the ideal. We will see that this is indeed the case, and prove it by lifting the multigraded resolution of an ideal, or more generally of a multigraded module, keeping track of how the shifts ‘deform’' in such a lifting; see Theorem 2·1 and Corollary 2·2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 2 , September 1995 , pp. 245 - 257
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

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