Mathematics – Commutative Algebra
Scientific paper
2007-01-06
Mathematics
Commutative Algebra
16 pages; corrected version
Scientific paper
Let S be a polynomial ring and R=S/I where I is a graded ideal of S. The Multiplicity Conjecture of Herzog, Huneke, and Srinivasan which was recently proved using the Boij-Soederberg 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 as 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.
No associations
LandOfFree
Betti numbers and shifts in minimal graded free resolutions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Betti numbers and shifts in minimal graded free resolutions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Betti numbers and shifts in minimal graded free resolutions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-305615