منابع مشابه
Upper 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...
متن کاملMultigraded 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.
متن کاملExtremal Betti numbers of graded modules 1 Marilena Crupi
Let S be a polynomial ring in n variables over a field K of characteristic 0. A numerical characterization of all possible extremal Betti numbers of any graded submodule of a finitely generated graded free S-module is given. 2010 Mathematics Subject Classification: 13B25, 13D02, 16W50.
متن کاملBetti Numbers of Graded Modules and Cohomology of Vector Bundles
In a remarkable paper Mats Boij and Jonas Söderberg [2006] conjectured that the Betti table of a Cohen-Macaulay module over a polynomial ring is a positive linear combination of Betti tables of modules with pure resolutions. We prove a strengthened form of their Conjectures. Applications include a proof of the Multiplicity Conjecture of Huneke and Srinivasan and a proof of the convexity of a fa...
متن کاملGRADED BETTI NUMBERS AND h-VECTORS OF LEVEL MODULES
Abstract. We study h-vectors and graded Betti numbers of level modules up to multiplication by a rational number. Assuming a conjecture on the possible graded Betti numbers of Cohen-Macaulaymodules we get a description of the possible h-vectors of level modules up to multiplication by a rational number. We also determine, again up to multiplication by a rational number, the cancellable h-vector...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1991
ISSN: 0021-8693
DOI: 10.1016/0021-8693(91)90103-f