Extensions of the Multiplicity conjecture

Migliore, Juan; Nagel, Uwe; Römer, Tim

doi:10.1090/S0002-9947-07-04360-7

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
DOI: https://doi.org/10.1090/S0002-9947-07-04360-7
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 -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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