Betti Numbers and Degree Bounds for Some Linked Zero-Schemes

2005/10/26 by Gold, Leah, Schenck, Hal, Srinivasan, Hema
#13D02 #13H15 #14M06 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0510552

Abstract

In their paper on multiplicity bounds (1998), 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 (1985). 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 I_Y.

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