Journal de théorie et applications du mensonge généralisé

Generalized Matric Massey Products for Graded Modules

Abstract

Arvid Siqveland

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.