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Published online by Cambridge University Press:  18 March 2013

David Eisenbud
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA email eisenbud@math.berkeley.edu
Daniel Erman
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109-1043, USA email erman@umich.edu
Frank-Olaf Schreyer
Affiliation:
Mathematik und Informatik, Universität des Saarlandes, Campus E2 4, D-66123 Saarbrücken, Germany email schreyer@math.uni-sb.de
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Abstract

A recent result of Eisenbud–Schreyer and Boij–Söderberg proves that the Betti diagram of any graded module decomposes as a positive rational linear combination of pure diagrams. When does this numerical decomposition correspond to an actual filtration of the minimal free resolution? Our main result gives a sufficient condition for this to happen. We apply it to show the non-existence of free resolutions with some plausible-looking Betti diagrams and to study the semigroup of quiver representations of the simplest ‘wild’ quiver.

Type
Research Article
Copyright
© The Author(s) 2013 

References

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