Graded Betti numbers of Cohen-Macaulay modules and the multiplicity conjecture
نویسندگان
چکیده
منابع مشابه
Betti Numbers of Graded Modules and the Multiplicity Conjecture in the Non-cohen-macaulay Case
Abstract. We use the results by Eisenbud and Schreyer [3] to prove that any Betti diagram of a graded module over a standard graded polynomial ring is a positive linear combination Betti diagrams of modules with a pure resolution. This implies the Multiplicity Conjecture of Herzog, Huneke and Srinivasan [5] for modules that are not necessarily Cohen-Macaulay. We give a combinatorial proof of th...
متن کاملGraded Betti Numbers of Cohen-macaulay Modules and the Multiplicity Conjecture
We give conjectures on the possible graded Betti numbers of Cohen-Macaulay modules up to multiplication by positive rational numbers. The idea is that the Betti diagrams should be non-negative linear combinations of pure diagrams. The conjectures are verified in the cases where the structure of resolutions are known, i.e., for modules of codimension two, for Gorenstein algebras of codimension t...
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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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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2008
ISSN: 0024-6107
DOI: 10.1112/jlms/jdn013