Koszul bicomplexes and generalized Koszul complexes in projective dimension one

Autor(en): Ichim, Bogdan
Vetter, Udo
Stichwörter: complexes; FREE RESOLUTIONS; Koszul complex; Mathematics
Erscheinungsdatum: 2006
Herausgeber: TAYLOR & FRANCIS INC
Journal: COMMUNICATIONS IN ALGEBRA
Volumen: 34
Ausgabe: 11
Startseite: 4131
Seitenende: 4156
Zusammenfassung: 
We describe Koszul type complexes associated with a linear map from any module to a free module, and vice versa with a linear map from a free module to an arbitrary module, generalizing tire classical Koszul complexes. Given a short complex of finite free modules, we assemble these complexes to what we call Koszul bicomplexes. They are used in order to investigate the homology of the Koszul complexes in projective dimension one. As in the case of the classical Koszul complexes, this homology turns out to be grade sensitive. In a special setup, we obtain necessary conditions for a map of free modules to be lengthened to a short complex of free modules.
ISSN: 00927872
DOI: 10.1080/00927870600876284

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