TY - JOUR

T1 - Betti numbers and degree bounds for some linked zero-schemes

AU - Gold, Leah

AU - Schenck, Hal

AU - Srinivasan, Hema

N1 - Funding Information:
Macaulay 2 computations provided evidence for the results in this paper. The first author thanks the University of Missouri for supporting her visit during the fall of 2003, when portions of this work were performed. 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.

PY - 2007/8

Y1 - 2007/8

N2 - 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 I in a polynomial ring R and the degree of I. 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 / I is Cohen-Macaulay, we may reduce to the case where I defines a zero-dimensional subscheme Y. If Y is residual to a zero-scheme Z of a certain type (low degree or points in special position), then we show that the conjecture is true for IY.

AB - 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 I in a polynomial ring R and the degree of I. 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 / I is Cohen-Macaulay, we may reduce to the case where I defines a zero-dimensional subscheme Y. If Y is residual to a zero-scheme Z of a certain type (low degree or points in special position), then we show that the conjecture is true for IY.

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U2 - 10.1016/j.jpaa.2006.10.017

DO - 10.1016/j.jpaa.2006.10.017

M3 - Article

AN - SCOPUS:33947239845

VL - 210

SP - 481

EP - 491

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 2

ER -