A deformation theory approach to Betti numbers of finite length modules (Q1178059)

Let \(M\) be a finite length \(R\)-module, where \(R=k[X_ 1,\ldots,X_ n]\). \textit{D. A. Buchsbaum} and \textit{D. Eisenbud} [Am. J. Math. 99, 447-485 (1977; Zbl 0373.13006)] conjecture that the \(i\)-th Betti number, \(\beta_ i\) of \(M\) should be at least \(n\choose i\). The authors prove this if \(M=R/I\) and \(I\) is an ideal generated by monomials. Then the result and technique of a paper by \textit{C. Huneke} and \textit{B. Ulrich} [Ann. Math., II. Ser. 126, 277-334 (1987; Zbl 0638.13003)] are extended.