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.

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.

DOI

10.1016/j.jpaa.2006.10.017

Version

Postprint

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Volume

210

Issue

2

Included in

Mathematics Commons

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