A Generalized Koszul Complex. II. Depth and Multiplicity
نویسندگان
چکیده
منابع مشابه
A Generalized Koszul Complex. I
Introduction. In [1], the Koszul complex was used to study the relationship between codimension and multiplicity. It also helped us investigate Macaulay modules and rings, and provided a context in which to prove the Cohen-Macaulay Theorem concerning the unmixedness of complete intersections. Now there is a generalization of the Cohen-Macaulay Theorem (known, we believe, as the generalized Cohe...
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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...
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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...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1964
ISSN: 0002-9947
DOI: 10.2307/1994241