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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