BETTI NUMBERS AND SHIFTS IN MINIMAL GRADED FREE RESOLUTIONS

DC FieldValueLanguage
dc.contributor.authorRoemer, Tim
dc.date.accessioned2021-12-23T15:56:22Z-
dc.date.available2021-12-23T15:56:22Z-
dc.date.issued2010
dc.identifier.issn00192082
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/2312-
dc.description.abstractLet 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.
dc.language.isoen
dc.publisherUNIV ILLINOIS URBANA-CHAMPAIGN
dc.relation.ispartofILLINOIS JOURNAL OF MATHEMATICS
dc.subjectBOUNDS
dc.subjectIDEALS
dc.subjectMathematics
dc.subjectMODULES
dc.subjectMULTIPLICITY CONJECTURE
dc.subjectPURE
dc.titleBETTI NUMBERS AND SHIFTS IN MINIMAL GRADED FREE RESOLUTIONS
dc.typejournal article
dc.identifier.doi10.1215/ijm/1318598667
dc.identifier.isiISI:000298441200002
dc.description.volume54
dc.description.issue2
dc.description.startpage449
dc.description.endpage467
dc.publisher.placeDEPT MATH, 1409 W GREEN ST, URBANA, IL 61801 USA
dcterms.isPartOf.abbreviationIll. J. Math.
dcterms.oaStatusGreen Submitted, hybrid
crisitem.author.deptFB 06 - Mathematik/Informatik-
crisitem.author.deptidfb06-
crisitem.author.parentorgUniversität Osnabrück-
crisitem.author.netidRoTi119-
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