Filtering free resolutions. (May 2013)

• Record Type: Journal Article
• Authors: Eisenbud, David; Erman, Daniel; Schreyer, Frank-Olaf
• Is Part Of: Compositio mathematica. Volume 149:Number 5(2013)
• Page Start: 754
• Page End: 772
• Publication Date: 2013-05
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X12000760
• Languages: English
• ISSNs: 0010-437X

Abstract

<abstract abstract-type="normal"> <title>Abstract</title> <p>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.</p> </abstract>