What is the Rees algebra of a module?
Authors:
David Eisenbud, Craig Huneke and Bernd Ulrich
Journal:
Proc. Amer. Math. Soc. 131 (2003), 701708
MSC (2000):
Primary 13A30, 13B21; Secondary 13C12
Published electronically:
September 17, 2002
MathSciNet review:
1937406
Fulltext PDF Free Access
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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 may be computed in terms of a ``maximal'' map from to a free module as the image of the map induced by on symmetric algebras. We show that the analytic spread and reductions of can be determined from any embedding of into a free module, and in characteristic 0but not in positive characteristic!the Rees algebra itself can be computed from any such embedding.
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Additional Information
David Eisenbud
Affiliation:
Mathematical Sciences Research Institute, 1000 Centennial Dr., Berkeley, California 94720
Email:
de@msri.org
Craig Huneke
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email:
huneke@math.ukans.edu
Bernd Ulrich
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email:
ulrich@math.purdue.edu
DOI:
http://dx.doi.org/10.1090/S0002993902065759
PII:
S 00029939(02)065759
Keywords:
Rees algebra,
module,
integral dependence
Received by editor(s):
May 2, 2001
Received by editor(s) in revised form:
October 19, 2001
Published electronically:
September 17, 2002
Additional Notes:
All three authors were partially supported by the NSF
Communicated by:
Wolmer V. Vasconcelos
Article copyright:
© Copyright 2002
American Mathematical Society
