Koszul Bicomplexes and Generalized Koszul Complexes in Projective Dimension One
نویسندگان
چکیده
منابع مشابه
Koszul Bicomplexes and Generalized Koszul Com- Plexes in Projective Dimension One
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 the 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 comp...
متن کاملThe Koszul Complex in Projective Dimension One
Let R be a noetherian ring and M a finite R-module. With a linear form χ on M one associates the Koszul complex K(χ). If M is a free module, then the homology of K(χ) is well-understood, and in particular it is grade sensitive with respect to Imχ. In this note we investigate the case of a module M of projective dimension 1 (more precisely, M has a free resolution of length 1) for which the firs...
متن کاملThe Koszul Complex in Projective Dimension One
Let R be a noetherian ring andM a finite R-module. With a linear form χ onM one associates the Koszul complex K(χ). IfM is a free module, then the homology of K(χ) is well-understood, and in particular it is grade sensitive with respect to Imχ. In this note we investigate the case of a module M of projective dimension 1 (more precisely, M has a free resolution of length 1) for which the first n...
متن کاملGeneralized Koszul Complexes
This article should be viewed as a survey of generalized Koszul complexes and Koszul bicomplexes with an application to generalized Koszul complexes in projective dimension one. We shall try to give detailed information on the basic definitions and a summary of the main results. Concerning proofs the reader is invited to have a look into [I] or [IV]. Introduction. We start with the following qu...
متن کاملKoszul Algebras and Sheaves over Projective Space
We are going to show that the sheafication of graded Koszul modules KΓ over Γn = K [x0, x1...xn] form an important subcategory ∧ KΓ of the coherents sheaves on projective space, Coh(P n). One reason is that any coherent sheave over P n belongs to ∧ KΓup to shift. More importantly, the category KΓ allows a concept of almost split sequence obtained by exploiting Koszul duality between graded Kosz...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2006
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870600876284