Jornal de Teoria Generalizada de Mentiras e Aplicações

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.