Free complexes defining maximal quasi-Buchsbaum graded modules over polynomial rings
The author investigates the structure of graded maximal quasi-Buchsbaum modules (MQB-modules, for short) over Gorenstein graded rings. The main results are the theorems (4.5) and (4.10) in section 4. Theorem (4.5) provides a sufficient condition for decomposability of an MQB-module of limite projective dimension; this condition states that (for each \(i)\) the set of all degrees in which the \(i\)-th graded local cohomology of the module does not vanish should be `decomposable' (in a certain sense). Under the extra assumption that at most two local cohomology modules do not vanish and each of them is concentrated in only one degree, there are even more explicit structure results for the given MQB-module (theorem (1.10)). The author's method to prove results about the given module \(M\) is to associate a certain minimal complex of finitely generated free modules to \(M\) and to investigate the structure of those complexes (in sections 2 and 3). At appropriate places the author explains connections and overlappings with recent papers of Yoshino and Cipu, Herzog, Popescu (preprints).
structure of graded maximal quasi- Buchsbaum modules
scientific article; zbMATH DE number 408741