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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Betti numbers of graded modules and cohomology of vector bundles
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by David Eisenbud and Frank-Olaf Schreyer PDF
J. Amer. Math. Soc. 22 (2009), 859-888 Request permission

Abstract:

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.

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Additional Information
  • David Eisenbud
  • Affiliation: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
  • MR Author ID: 62330
  • ORCID: 0000-0002-5418-5579
  • Email: eisenbud@math.berkeley.edu
  • Frank-Olaf Schreyer
  • Affiliation: Mathematik und Informatik, Universität des Saarlandes, Campus E2 4, D-66123 Saarbrücken, Germany
  • MR Author ID: 156975
  • Email: schreyer@math.uni-sb.de
  • Received by editor(s): January 17, 2008
  • Published electronically: October 27, 2008

  • Dedicated: Dedicated to Mark Green, whose work connecting Algebraic Geometry and Free Resolutions has inspired us for a quarter of a century, on the occasion of his sixtieth birthday
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 22 (2009), 859-888
  • MSC (2000): Primary 14F05, 13D02; Secondary 13D25, 14N99
  • DOI: https://doi.org/10.1090/S0894-0347-08-00620-6
  • MathSciNet review: 2505303