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The Dedekind-Mertens formula and determinantal rings
Author(s):
Winfried
Bruns;
Anna
Guerrieri
Journal:
Proc. Amer. Math. Soc.
127
(1999),
657-663.
MSC (1991):
Primary 13C40, 13C14, 13D40, 13P10
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Abstract:
We give a combinatorial proof of the Dedekind-Mertens formula by computing the initial ideal of the content ideal of the product of two generic polynomials. As a side effect we obtain a complete classification of the rank  Cohen-Macaulay modules over the determinantal rings ![$K[X]/I_2(X)$](/proc/1999-127-03/S0002-9939-99-04535-9/gif-abstract/img2.gif) .
References:
- 1.
- D. Bayer and M. Stillman. Macaulay: a system for computation in algebraic geometry and commutative algebra. Available by anonymous ftp from zariski.harvard.edu.
- 2.
- G. Boffi, W. Bruns, and A. Guerrieri. On the jacobian ideal of a trilinear form. Preprint.
- 3.
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- A. Conca and J. Herzog. On the Hilbert function of determinantal rings and their canonical module. Proc. Amer. Math. Soc. 122 (1994), 677-681. MR 95a:13016
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Additional Information:
Winfried
Bruns
Affiliation:
Universität Osnabrück, FB Mathematik/Informatik, 49069 Osnabrück, Germany
Email:
Winfried.Bruns@mathematik.uni-osnabrueck.de
Anna
Guerrieri
Affiliation:
Università di L'Aquila, Dip. di Matematica, Via Vetoio, Coppito, 67010 L'Aquila, Italy
Email:
guerran@univaq.it
DOI:
10.1090/S0002-9939-99-04535-9
PII:
S 0002-9939(99)04535-9
Keywords:
Dedekind--Mertens formula,
initial ideal,
determinantal ring,
Cohen--Macaulay module
Received by editor(s):
January 22, 1997
Received by editor(s) in revised form:
June 16, 1997
Additional Notes:
The visit of the first author to the University of L'Aquila that made this paper possible was supported by the Vigoni program of the DAAD and the CRUI
Communicated by:
Wolmer V. Vasconcelos
Copyright of article:
Copyright
1999,
American Mathematical Society
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