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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geprüft am 12.05.2024