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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Extensions of the Multiplicity conjecture


Authors: Juan Migliore, Uwe Nagel and Tim Römer
Journal: Trans. Amer. Math. Soc. 360 (2008), 2965-2985
MSC (2000): Primary 13H15, 13D02; Secondary 13C40, 14M12, 13C14, 14H50
Published electronically: November 28, 2007
MathSciNet review: 2379783
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Abstract: The Multiplicity conjecture of Herzog, Huneke, and Srinivasan states an upper bound for the multiplicity of any graded $ k$-algebra as well as a lower bound for Cohen-Macaulay algebras. In this note we extend this conjecture in several directions. We discuss when these bounds are sharp, find a sharp lower bound in the case of not necessarily arithmetically Cohen-Macaulay one-dimensional schemes of 3-space, and propose an upper bound for finitely generated graded torsion modules. We establish this bound for torsion modules whose codimension is at most two.


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Additional Information

Juan Migliore
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: Juan.C.Migliore.1@nd.edu

Uwe Nagel
Affiliation: Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, Kentucky 40506-0027
Email: uwenagel@ms.uky.edu

Tim Römer
Affiliation: FB Mathematik/Informatik, Universität Osnabrück, 49069 Osnabrück, Germany
Email: troemer@uos.de

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04360-7
PII: S 0002-9947(07)04360-7
Received by editor(s): March 2, 2006
Published electronically: November 28, 2007
Additional Notes: Part of the work for this paper was done while the first author was sponsored by the National Security Agency under Grant Number MDA904-03-1-0071
Article copyright: © Copyright 2007 American Mathematical Society