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Extended degree functions and monomial modules
Author(s):
Uwe
Nagel;
Tim
Römer
Journal:
Trans. Amer. Math. Soc.
358
(2006),
3571-3589.
MSC (2000):
Primary 13D40, 13C99;
Secondary 13P10, 13H10
Posted:
December 20, 2005
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Additional information
Abstract:
The arithmetic degree, the smallest extended degree, and the homological degree are invariants that have been proposed as alternatives of the degree of a module if this module is not Cohen-Macaulay. We compare these degree functions and study their behavior when passing to the generic initial or the lexicographic submodule. This leads to various bounds and to counterexamples to a conjecture of Gunston and Vasconcelos, respectively. Particular attention is given to the class of sequentially Cohen-Macaulay modules. The results in this case lead to an algorithm that computes the smallest extended degree.
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Additional Information:
Uwe
Nagel
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027
Email:
uwenagel@ms.uky.edu
Tim
Römer
Affiliation:
FB Mathematik/Informatik, Universität Osnabrück, 49069 Osnabrück, Germany
Email:
troemer@mathematik.uni-osnabrueck.de
DOI:
10.1090/S0002-9947-05-03848-1
PII:
S 0002-9947(05)03848-1
Keywords:
Extended degree functions,
Buchsbaum module,
sequentially Cohen-Macaulay module,
generic initial module,
lexicographic module,
bounds for degree functions
Received by editor(s):
June 21, 2004
Received by editor(s) in revised form:
August 8, 2004
Posted:
December 20, 2005
Additional Notes:
The first author gratefully acknowledges partial support by a Special Faculty Research Fellowship from the University of Kentucky.
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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