Graded Betti numbers of Cohen-Macaulay modules and the Multiplicity conjecture

Details Graded Betti numbers of Cohen-Macaulay modules and the Multiplicity conjecture Graded Betti numbers of Cohen-Macaulay modules and the Multiplicity conjecture

2006-11-03

arxiv.org/abs/math/0611081v2

Mathematics

Commutative Algebra

24 pages, references and examples added

Scientific paper

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 three and for complete intersections. The motivation for the conjectures comes from the Multiplicity conjecture of Herzog, Huneke and Srinivasan.

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