Upper Bounds for the Betti Numbers of a given Hilbert Function

Details Upper Bounds for the Betti Numbers of a given Hilbert Function Upper Bounds for the Betti Numbers of a given Hilbert Function

1992-05-19

arxiv.org/abs/alg-geom/9205006v1

Mathematics

Algebraic Geometry

18 pages, plain tex

Scientific paper

From a Macaulay's paper it follows that a lex-segment ideal has the greatest number of generators (the 0-th Betti number $\b_0$) among all the homogeneous ideals with the same Hilbert function. In this paper we prove that this fact extends to every Betti number, in the sense that all the Betti numbers of a minimal free resolution of a lex segment ideal are bigger than or equal to the ones of any homogeneous ideal with the same Hilbert function.

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