Resolutions obtained by iterated mapping cones (Q1902095)

The authors introduce the notion of lex-seq plus \(s\)-powers ideals, obtained from lex-seg ideals by adding \(s\) powers of distinct indeterminates; and that of lex-seg with holes ideals, derived from lex-seg ideals by removing suitable monomials (namely: those whose exponent on some of the indeterminates is higher than a bound previously fixed for that indeterminate). By taking a subcomplex of the one constructed by Eliahou and Kervaire, the authors exhibit a minimal resolution for lex-seg with holes ideals; then, by adding the powers one at a time and iterating mapping cones, they find a minimal resolution for lex-seg plus \(s\)-powers ideals. Lex-seg plus \(s\)-powers ideals were mentioned in a paper by \textit{D. Eisenbud, M. Green} and \textit{J. Harris} [in: Journées géométrie algébrique, Astérisque 218, 187-202 (1993; Zbl 0819.14001)] for making sharp \(a\) a conjecture of theirs (conjecture \(V_m)\) about a bound for the growth of the Hilbert function.