Betti Numbers of Graded Modules and the Multiplicity Conjecture in the Non-cohen-macaulay Case
نویسندگان
چکیده
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 the convexity of the simplicial fan spanned by the pure diagrams.
منابع مشابه
Graded 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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