The splitting principle and singularities
arXiv:1108.1586
Abstract
The splitting principle states that morphisms in a derived category do not "split" accidentally. This has been successsfully applied in several characterizations of rational, DB, and other singularities. In this article I prove a general statement that implies many of the previous individual statements and improves some of the characterizations in the process.
12 pages. To appear in the volume on "Compact moduli spaces and vector bundles"