What is the Rees Algebra of a Module?
Commutative Algebra
2007-05-23 v1 Algebraic Geometry
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.
Cite
@article{arxiv.math/0209187,
title = {What is the Rees Algebra of a Module?},
author = {David Eisenbud and Craig Huneke and Bernd Ulrich},
journal= {arXiv preprint arXiv:math/0209187},
year = {2007}
}
Comments
8 pages, AMS-TeX. Accepted 8/2001 for the Proceedings of the American Mathematical Society