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A note on the Buchsbaum-Rim multiplicity of a parameter module
Authors:
Futoshi Hayasaka and Eero Hyry
Journal:
Proc. Amer. Math. Soc. 138 (2010), 545-551
MSC (2000):
Primary 13H15; Secondary 13D25
Posted:
September 29, 2009
MathSciNet review:
2557171
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Additional Information
Abstract: In this article we prove that the Buchsbaum-Rim multiplicity  of a parameter module  in a free module  is bounded above by the colength  . Moreover, we prove that once the equality  holds true for some parameter module  in  , then the base ring  is Cohen-Macaulay.
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- W. Bruns and U. Vetter, Length formulas for the local cohomology of exterior powers, Math. Z. 191 (1986), 145-158. MR 812608 (87c:13016)
- 2.
- W. Bruns and U. Vetter, Determinantal Rings, Lecture Notes in Math., 1327, Springer-Verlag, Berlin-Heidelberg, 1988. MR 953963 (89i:13001)
- 3.
- D. A. Buchsbaum and D. Eisenbud, Generic free resolutions and a family of generically perfect ideals, Adv. in Math. 18 (1975), 245-301. MR 0396528 (53:391)
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- D. A. Buchsbaum and D. S. Rim, A generalized Koszul complex, Bull. Amer. Math. Soc. 69 (1963), 382-385. MR 0148720 (26:6226)
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- D. Eisenbud, Commutative algebra. With a view toward algebraic geometry, Graduate Texts in Mathematics, 150, Springer-Verlag, New York, 1995. MR 1322960 (97a:13001)
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- D. Kirby, A sequence of complexes associated with a matrix, J. London Math. Soc. 7 (1974), 523-530. MR 0337939 (49:2708)
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- J-P. Serre, Local Algebra (translated from the French by CheeWhye Chin), Springer Monographs in Mathematics, Springer-Verlag, Berlin-Heidelberg, 2000. MR 1771925 (2001b:13001)
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- J. Stückrad and W. Vogel, Buchsbaum Rings and Applications, Springer-Verlag, Berlin-Heidelberg-New York-London-Paris-Tokyo, 1986. MR 881220 (88h:13011a)
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Additional Information
Futoshi Hayasaka
Affiliation:
Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki 214–8571, Japan
Email:
hayasaka@isc.meiji.ac.jp
Eero Hyry
Affiliation:
Department of Mathematics and Statistics, University of Tampere, 33014 Tampereen yliopisto, Finland
Email:
Eero.Hyry@uta.fi
DOI:
http://dx.doi.org/10.1090/S0002-9939-09-10119-3
PII:
S 0002-9939(09)10119-3
Keywords:
Buchsbaum-Rim multiplicity,
parameter module,
Euler-Poincar\'e characteristic,
generalized Koszul complex
Received by editor(s):
August 17, 2008
Received by editor(s) in revised form:
July 14, 2009
Posted:
September 29, 2009
Communicated by:
Bernd Ulrich
Article copyright:
© Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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