Filtering free resolutions

Details Filtering free resolutions Filtering free resolutions

2010-01-04

arxiv.org/abs/1001.0585v2

Mathematics

Commutative Algebra

This is a major revision. The main results have been strengthened and clarified, and we have completely rewritten the introduc

Scientific paper

A recent result of Eisenbud-Schreyer and Boij-S\"oderberg 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.

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