Extensions of the multiplicity conjecture
Autor(en): | Migliore, Juan Nagel, Uwe Roemer, Tim |
Stichwörter: | ALGEBRAS; BETTI NUMBERS; BOUNDS; IDEALS; LIAISON; Mathematics | Erscheinungsdatum: | 2008 | Herausgeber: | AMER MATHEMATICAL SOC | Journal: | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | Volumen: | 360 | Ausgabe: | 6 | Startseite: | 2965 | Seitenende: | 2985 | Zusammenfassung: | 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. |
ISSN: | 00029947 |
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