Extensions of the Multiplicity Conjecture

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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 case of not necessarily arithmetically Cohen-Macaulay one-dimensional schemes of 3-space, and we propose an upper bound for finitely generated graded torsion modules. We establish this bound for torsion modules whose codimension is at most two.
22 pages

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Commutative Algebra, Algebraic Geometry, 13D02; 13H15; 13C40

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http://salesiana.dossiersoluciones.com/handle/123456789/75156

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0505229
 http://arxiv.org/abs/math/0505229

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arXiv