Generalized Matric Massey Products for Graded ModulesArvid Siqveland
Buskerud University College, Department of Technology, P.O. Box 251, N-3601 Kongsberg, Norway Email: [email protected]
Received date: 1 October 2009; Accepted date: 10 December 2010
The theory of generalized matric Massey products has been applied for some time to A-modules M, A being a k-algebra. The main application is to compute the local formal moduli ˆHM, isomorphic to the local ring of the moduli of A-modules. This theory is also generalized to OX-modulesM, X being a k-scheme. In these notes, we consider the definition of generalized Massey products and the relation algebra in any obstruction situation (a differential graded k-algebra with certain properties), and prove that this theory applies to the case of graded Rmodules, R being a graded k-algebra and k algebraically closed. When the relation algebra is algebraizable, that is, the relations are polynomials rather than power series, this gives a combinatorial way to compute open (´etale) subsets of the moduli of graded R-modules. This also gives a sufficient condition for the corresponding point in the moduli of O Proj(R)-modules to be singular. The computations are straightforwardly algorithmic, and an example on the postulation Hilbert scheme is given.