Betti Numbers of Graded Modules and Cohomology of Vector Bundles

Details Betti Numbers of Graded Modules and Cohomology of Vector Bundles Betti Numbers of Graded Modules and Cohomology of Vector Bundles

2007-12-11

arxiv.org/abs/0712.1843v3

Mathematics

Commutative Algebra

This version incorporates many corrections and many expository improvements of the original. It is to appear in the Journal of

Scientific paper

Mats Boij and Jonas Soederberg (math.AC/0611081) have conjectured that the Betti table of a Cohen-Macaulay module over a polynomial ring can be decomposed in a certain way as a positive linear combination of Betti tables of modules with pure resolutions. We prove, over any field, a strengthened form of their conjecture. Applications include a proof of the Multiplicity Conjecture of Huneke and Srinivasan and a proof of the convexity of a fan naturally associated to the Young lattice. We also characterize the rational cone of all cohomology tables of vector bundles on projective spaces in terms of the cohomology tables of "supernatural" bundles. This characterization is dual, in a certain sense, to our characterization of Betti tables.

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