Gluing Cohen-Macaulay modules with applications to quasihomogeneous complete intersections with isolated singularities (Q1313257)

This paper deals with the problem of characterizing quasihomogeneous isolated singularities. The history begins in 1971 with the beautiful result of \textit{K. Saito} [Invent. Math. 14, 123-142 (1971; Zbl 0224.32011)]: an isolated complex hypersurface singularity with defining equation \(f\) is quasihomogeneous (i.e., after a change of coordinates \(f\) can be made into a quasihomogeneous polynomial) if and only if \(f \in j(f)\), where \(j(f)\) is the ideal generated by the partial derivative of \(f\) (this ideal is also called the jacobian ideal of \(f)\). -- In the subsequent years this result was extended to other fields and significantly generalized. In this paper we further explore the properties of quasihomogeneous isolated singularities via module-theoretic techniques. Our main tool is what we call the gluing construction for Cohen-Macaulay modules which produces minimal Cohen-Macaulay approximations (and, if the ring is Gorenstein, hulls of finite injective dimension) for (nonmaximal) Cohen- Macaulay modules and their syzygy modules.