Extensions of the Multiplicity conjecture

• Autores: Juan C. Migliore, Uwe Nagel , Tim Römer
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 360, Nº 6, 2008, págs. 2965-2985
• Idioma: inglés
• DOI: 10.1090/S0002-9947-07-04360-7
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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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