Ideals Whose First Two Betti Numbers are Close

Details Ideals Whose First Two Betti Numbers are Close Ideals Whose First Two Betti Numbers are Close

2010-03-02

arxiv.org/abs/1003.0544v3

Mathematics

Commutative Algebra

9 pages

Scientific paper

For an ideal $I$ of a Noetherian local ring $(R,\fm,k)$ we show that
$\bt_1^R(I)-\bt_0^R(I)\geq -1$. It is demonstrated that some residual
intersections of an ideal $I$ for which $\bt_1^R(I)-\bt_0^R(I)=
-1\;\text{or}\;0$ are perfect. Some relations between Betti numbers and Bass
numbers of the canonical module are studied.

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