منابع مشابه
Multigraded Modules
Let R = k[x1, . . . , xn] be a polynomial ring over a field k. We present a characterization of multigraded R-modules in terms of the minors of their presentation matrix. We describe explicitly the second syzygies of any multigraded R-module.
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The Stanley’s Conjecture on Cohen-Macaulay multigraded modules is studied especially in dimension 2. In codimension 2 similar results were obtained by Herzog, Soleyman-Jahan and Yassemi. As a consequence of our results Stanley’s Conjecture holds in 5 variables.
متن کاملShifts in Resolutions of Multigraded Modules
Upper bounds are established on the shifts in a minimal resolution of a multigraded module. Similar bounds are given on the coefficients in the numerator of the BackelinLescot rational expression for multigraded Poincaré series. Let K be a field and S = K[x1, . . . , xn] the polynomial ring with its natural n-grading. When I is an ideal generated by monomials in the variables x1, . . . , xn, th...
متن کاملRegularity and Resolutions for Multigraded Modules
This paper is concerned with the relationships between two concepts, vanishing of cohomology groups and the structure of free resolutions. In particular, we study the connection between vanishing theorems for the local cohomology of multigraded modules and the structure of their free multigraded resolutions.
متن کاملUpper Bounds for Betti Numbers of Multigraded Modules
This paper gives a sharp upper bound for the Betti numbers of a finitely generated multigraded R-module, where R = k[x1, . . . , xm] is the polynomial ring over a field k in m variables. The bound is given in terms of the rank and the first two Betti numbers of the module. An example is given which achieves these bounds simultaneously in each homological degree. Using Alexander duality, a bound...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2008
ISSN: 0019-2082
DOI: 10.1215/ijm/1258554354