BETTI NUMBERS AND SHIFTS IN MINIMAL GRADED FREE RESOLUTIONS

Autor(en): Roemer, Tim 
Stichwörter: BOUNDS; IDEALS; Mathematics; MODULES; MULTIPLICITY CONJECTURE; PURE
Erscheinungsdatum: 2010
Herausgeber: UNIV ILLINOIS URBANA-CHAMPAIGN
Journal: ILLINOIS JOURNAL OF MATHEMATICS
Volumen: 54
Ausgabe: 2
Startseite: 449
Seitenende: 467
Zusammenfassung: 
Let S = K[x(1), ... , x(n)] be a polynomial ring and R=S/1 where 1 subset of S is a graded ideal. The Multiplicity Conjecture of Herzog. Huneke, and Srinivasan winch was recently proved using the Boij-Soderberg theory states 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 as well as bounded below by a function of the minimal shifts if R is Cohen-Macaulay. In this paper, we study the related problem to show that the total Betti-numbers of R are also bounded above by a function of the shifts in the minimal graded free resolution of R its well as bounded below by another function of the shifts if R is Cohen-Macaulay. We also discuss the cases when these bounds are sharp.
ISSN: 00192082
DOI: 10.1215/ijm/1318598667

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