Document Type
Article
Publication Date
8-1-2007
Publication Title
Journal of Pure and Applied Algebra
Abstract
In [J. Herzog, H. Srinivasan, Bounds for multiplicities, Trans. Amer. Math. Soc. 350 (1998) 2879–2902], Herzog and Srinivasan study the relationship between the graded Betti numbers of a homogeneous ideal II in a polynomial ring RR and the degree of II. For certain classes of ideals, they prove a bound on the degree in terms of the largest and smallest Betti numbers, generalizing results of Huneke and Miller in [C. Huneke, M. Miller, A note on the multiplicity of Cohen–Macaulay algebras with pure resolutions, Canad. J. Math. 37 (1985) 1149–1162]. The bound is conjectured to hold in general; we study this using linkage. If R/IR/I is Cohen–Macaulay, we may reduce to the case where II defines a zero-dimensional subscheme YY. If YY is residual to a zero-scheme ZZ of a certain type (low degree or points in special position), then we show that the conjecture is true for IYIY.
Repository Citation
Gold, Leah; Schenck, Hal; and Srinivasan, Hema, "Betti Numbers and Degree Bounds for Some Linked Zero-Schemes" (2007). Mathematics and Statistics Faculty Publications. 165.
https://engagedscholarship.csuohio.edu/scimath_facpub/165
DOI
10.1016/j.jpaa.2006.10.017
Version
Postprint
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Volume
210
Issue
2
Comments
Gold is supported by an NSF-VIGRE postdoctoral fellowship. Schenck is supported by NSF Grant DMS 03-11142 and NSA Grant MDA 904-03-1-0006.