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Bulletin of the London Mathematical Society Advance Access originally published online on January 28, 2009
Bulletin of the London Mathematical Society 2009 41(1):79-88; doi:10.1112/blms/bdn106
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© 2009 London Mathematical Society

The Fitting ideal problem

A. Simis

Departamento de Matemática
CCEN
Universidade Federal de Pernambuco
50740-540 Recife
PE
Brazil

B. Ulrich

Department of Mathematics
Purdue University
West Lafayette, IN 47907
USA
ulrich@math.purdue.edu

Received 27 August 2007. Revision received 11 September 2008.

Let A be a Noetherian local ring and let E be a finitely generated A-module having rank r. In this note one deals with the expected inequality {ell}({wedge}rE) ≥ height (Fittr(E)), where height (Fittr(E)) is the codimension of the rth Fitting ideal of E, and {ell}(M) stands for the analytic spread of a module M. One establishes cases where the inequality holds as well as where it fails. A special case where the inequality holds implies the celebrated Zak inequality for the dimension of the image of the Gauss map.

Dedicated to Wolmer Vasconcelos on his 70th birthday

2000 Mathematics Subject Classification 13A30 (primary), 13B21, 13C12, 13C14, 13C40 (secondary).

The first author was partially supported by a grant from CNPq (Brazil). The second author was partially supported by the NSF; this author also thanks the Department of Mathematics of the Federal University of Pernambuco for its hospitality.


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