Ideals Whose First Two Betti Numbers are Close

Keivan Borna, S. H. Hassanzadeh

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 $…