Residual Intersections of Modules

Abstract: Motivated geometrically by the study of intersections of algebraic variety, the theory of linkage and residual intersections has plenty of beautiful applications to commutative algebra. For instance, linkage provides an interesting duality between ideals which preserves various homological properties, while residual intersections have proved to be an extremely useful tool to understand powers of ideals and integral dependence of Rees rings of ideals. When studying singularities of families of algebraic varieties, one faces the need to understand Rees rings associated with modules over a commutative ring and their integral dependence. However, the techniques used to study the problem in the case of ideals do not usually apply to the case of modules, so one needs to develop new tools. In this talk, I will discuss a notion of residual intersection for modules and their Cohen-Macaulay property. If time allows, I will also explore possible connections with some of the existing notions of linkage of modules. This is part of joint work with Louiza Fouli and Jooyoun Hong.

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