Betti numbers of graded modules and cohomology of vector bundles
By David Eisenbud, Frank-Olaf Schreyer. 2007
209 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/4bf629644d38db67f1050d765572d852a33a89d4
How researchers see this paper
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In Algebra and Number Theory
- L. Ein
- Gunnar Fløystad
- R. Lazarsfeld
- Jerzy Weyman
- David Eisenbud
- M. Mustaţă
- Robert J. Berman
- Morihiko Saito
In Geometry and Topology
- L. Ein
- R. Lazarsfeld
- Gunnar Fløystad
- Jerzy Weyman
- David Eisenbud
- M. Mustaţă
- Tommaso de Fernex
- Mattias Jonsson
Citations in the corpus
- Boij-Söderberg theory: Introduction and survey (2011, background): “And in December 2007 they published on the arXiv the proof of the second part of the conjectures of Boij and Söderberg, [12].”
- Asymptotic syzygies of algebraic varieties (2011, methodology): “16 On a fixed projective space, the work [12] of Eisenbud–Schreyer on the Boij–Soderberg conjecture gives an overall picture of the Betti tables that can arise.”
- The Existence of Pure Free Resolutions (2007, background): “The construction of Eisenbud-Schreyer [7] is complementary to this one, in that putting together the two equivariant examples produced here with the example produced there shows that this conjecture is true for many degree sequences.”