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What is the Rees Algebra of a Module?

David Eisenbud·Craig Huneke·Bernd Ulrich
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Abstract

In this paper we show that the Rees algebra can be made into a functor on modules over a ring in a way that extends its classical definition for ideals. The Rees algebra of a module M may be computed in terms of a "maximal" map f from M to a free module. It is the image of the map induced by f on symmetric algebras. We show that the analytic spread and reductions of M can be determined from any embedding of M into a free module, and in characteristic 0--but not in positive characteristic!--the Rees algebra itself can be computed from any such embedding.

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David Eisenbud, Craig Huneke, Bernd Ulrich. 2002-09-15. What is the Rees Algebra of a Module?. https://arxiv.org/abs/math/0209187

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