Minimal resolutions of some monomial submodules
The present paper studies the behaviour of extremal Betti numbers [\textit{D. Bayer, H. Charalambous} and \textit{S. Popescu}, J. Algebra 221, No. 2, 497--512 (1999; Zbl 0946.13008)] of some classes of monomial submodules. In particular, the authors focus on lexicographic submodules of finitely generated graded free S-modules of rank bigger than one with a homogeneous basis. The importance of these submodules comes from the results of \textit{H. A. Hulett} and \textit{K. Pardue} [Commun. Algebra 23, No. 4, 1249--1263 (1995; Zbl 0816.13012), Ill. J. Math. 40, No. 4, 564--585 (1996; Zbl 0903.13004)] that generalize to modules the famous results for ideals of Bigatti, Hulett and Pardue. The main contributions of the paper are Theorem 3.6, which states that a lexicographic submodule has at most two extremal Betti numbers and Theorem 4.5 that gives a characterization of the possible values of extremal Betti numbers of a lexicographic submodule.
scientific article; zbMATH DE number 5659731