منابع مشابه
Extremal 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.
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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...
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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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Upper bounds on the topological Betti numbers of Vietoris-Rips complexes are established, and examples of such complexes with high Betti
متن کاملCombinatorial Shifting and Graded Betti Numbers
Let ∆ be a simplicial complex and I∆ its Stanley–Reisner ideal. It has been conjectured that, for each i and j, the graded Betti number βii+j(I∆) of I∆ is smaller than or equal to that of I∆c , where ∆ c is a combinatorial shifted complex of ∆. In the present paper the conjecture will be proved affirmatively. In particular the inequalities βii+j(I∆) ≤ βii+j(I∆lex) hold for all i and j, where ∆ ...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2016
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2015.11.006