Extended degree functions and monomial modules

Autor(en): Nagel, Uwe
Roemer, Tim 
Stichwörter: BOUNDS; bounds for degree functions; Buchsbaum module; CASTELNUOVO-MUMFORD REGULARITY; CURVES; extended degree functions; generic initial module; IDEALS; lexicographic module; LOCAL COHOMOLOGY; Mathematics; sequentially Cohen-Macaulay module
Erscheinungsdatum: 2006
Herausgeber: AMER MATHEMATICAL SOC
Journal: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Volumen: 358
Ausgabe: 8
Startseite: 3571
Seitenende: 3589
Zusammenfassung: 
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.
ISSN: 00029947
DOI: 10.1090/S0002-9947-05-03848-1

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