Generalized Matric Massey Products for Graded Modules

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dc.creatorSiqveland, Arvid
dc.date2006-03-17
dc.date.accessioned2026-07-07T07:07:01Z
dc.date.available2026-07-07T07:07:01Z
dc.descriptionThe 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 $\hat{H}_M$, isomorphic to the local ring of the moduli of $A$-modules. This theory is also generalized to $\mathcal{O}_X$-modules $\mathcal{M}$, $X$ 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 $\mathcal{O}_{\Proj(R)}$-modules to be singular. The computations are straight forward, algorithmic, and an example on the postulation Hilbert scheme is given.
dc.identifierhttps://arxiv.org/abs/math/0603425
dc.identifierhttp://arxiv.org/abs/math/0603425
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110240
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subject14D15,13D10,13D02,13D07,14D22
dc.titleGeneralized Matric Massey Products for Graded Modules
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