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- Title
Filtering free resolutions.
- Authors
Eisenbud, David; Erman, Daniel; Schreyer, Frank-Olaf
- 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.
- Subjects
FREE resolutions (Algebra); MATHEMATICAL proofs; BETTI numbers; MODULES (Algebra); NUMERICAL analysis; MATHEMATICAL decomposition; EXISTENCE theorems; SEMIGROUPS (Algebra)
- Publication
Compositio Mathematica, 2013, Vol 149, Issue 5, p754
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X12000760