Note on bounds for multiplicities
Autor(en): | Romer, T | Stichwörter: | BETTI NUMBERS; COMPONENTWISE LINEAR IDEALS; Mathematics; Mathematics, Applied; RESOLUTIONS | Erscheinungsdatum: | 2005 | Herausgeber: | ELSEVIER SCIENCE BV | Journal: | JOURNAL OF PURE AND APPLIED ALGEBRA | Volumen: | 195 | Ausgabe: | 1 | Startseite: | 113 | Seitenende: | 123 | Zusammenfassung: | Let S = K[x(1),...,x(n)] be a polynomial ring and R = S/I be a graded K-algebra where I subset of S is a graded ideal. Herzog, Huneke and Srinivasan have conjectured that the multiplicity of R is bounded above by a function of the maximal shifts in the minimal graded free resolution of R over S. We prove the conjecture in the case that codim(R) = 2 which generalizes results in (J. Pure Appl. Algebra 182 (2003) 201; Trans. Amer. Math. Soc. 350 (1998) 2879). We also give a proof for the bound in the case in which I is componentwise linear. For example, stable and squarefree stable ideals belong to this class of ideals. (C) 2004 Elsevier B.V. All rights reserved. |
ISSN: | 00224049 | DOI: | 10.1016/j.jpaa.2004.05.008 |
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geprüft am 13.05.2024