منابع مشابه
Koszul Cycles
We prove regularity bounds for Koszul cycles holding for every ideal of dimension ≤ 1 in a polynomial ring; see Theorem 3.5. In Theorem 4.7 we generalize the “c + 1” lower bound for the Green–Lazarsfeld index of Veronese rings proved in (Bruns et al., arXiv:0902.2431) to the multihomogeneous setting. For the Koszul complex of the c-th power of the maximal ideal in a Koszul ring we prove that th...
متن کاملCastelnuovo-mumford Regularity for Complexes and Weakly Koszul Modules
Let A be a noetherian AS regular Koszul quiver algebra (if A is commutative, it is essentially a polynomial ring), and grA the category of finitely generated graded left A-modules. Following Jørgensen, we define the CastelnuovoMumford regularity reg(M•) of a complex M• ∈ D(grA) in terms of the local cohomologies or the minimal projective resolution of M•. Let A be the quadratic dual ring of A. ...
متن کاملOn Inverting the Koszul
Let V be an n-dimensional vector space. We give a direct construction of an exact sequence that gives a GL(V)-equivariant " resolution " of each symmetric power S t V in terms of direct sums of tensor products of the form ∧ i 1 V ⊗ · · · ⊗ ∧ ip V. This exact sequence corresponds to inverting the relation in the representation ring of GL(V) that is described by the Koszul complex, and has appear...
متن کاملA 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...
متن کاملPoincaré/koszul Duality
We prove a duality for factorization homology which generalizes both usual Poincaré duality for manifolds and Koszul duality for En-algebras. The duality has application to the Hochschild homology of associative algebras and enveloping algebras of Lie algebras. We interpret our result at the level of topological quantum field theory.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.07.013