Geodesic
Betti numbers of graded modules and cohomology of vector bundles
Eisenbud, David1 ; Schreyer, Frank-Olaf2
1 Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
2 Mathematik und Informatik, Universität des Saarlandes, Campus E2 4, D-66123 Saarbrücken, Germany
Journal of the American Mathematical Society, Tome 22 (2009) no. 3, pp. 859-888

Voir la notice de l'article provenant de la source American Mathematical Society

In the remarkable paper Graded Betti numbers of Cohen-Macaulay modules and the multiplicity conjecture, Mats Boij and Jonas Söderberg 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 fan naturally associated to the Young lattice. With the same tools we show that the cohomology table of any vector bundle on projective space is a positive rational linear combination of the cohomology tables of what we call supernatural vector bundles. Using this result we give new bounds on the slope of a vector bundle in terms of its cohomology.
DOI : 10.1090/S0894-0347-08-00620-6

Eisenbud, David 1 ; Schreyer, Frank-Olaf 2

1 Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
2 Mathematik und Informatik, Universität des Saarlandes, Campus E2 4, D-66123 Saarbrücken, Germany 
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Eisenbud, David; Schreyer, Frank-Olaf. Betti numbers of graded modules and cohomology of vector bundles. Journal of the American Mathematical Society, Tome 22 (2009) no. 3, pp. 859-888. doi: 10.1090/S0894-0347-08-00620-6

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