Betti Numbers and Degree Bounds for Some Linked ZeroSchemes
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 CohenMacaulay, we may reduce to the case where I defines a zerodimensional subscheme Y. If Y is residual to a zeroscheme Z of a certain type (low degree or points in special position), then we show that the conjecture is true for I_Y.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2005
 arXiv:
 arXiv:math/0510552
 Bibcode:
 2005math.....10552G
 Keywords:

 Mathematics  Commutative Algebra;
 13D02;
 14M06;
 13H15
 EPrint:
 12 pages