Generalized Matric Massey Products for Graded Modules

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The theory of generalized matric Massey products has been applied for some time to A-modules M, A a k-algebra. The main application is to compute the local formal moduli Hₘ, isomorphic to the local ring of the moduli of A-modules. This theory is also generalized to Oₓ-modules M, X 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 R-modules, R a graded k-algebra, 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 (étale) subsets of the moduli of graded R-modules. This also gives a sufficient condition for the corresponding point in the moduli of O(R)-modules to be singular. The computations are straight forward, algorithmic, and an example on the postulation Hilbert scheme is given.