Supernatural analogues of Beilinson monads. (14th November 2016)

• Record Type: Journal Article
• Authors: Erman, Daniel; Sam, Steven V
• Is Part Of: Compositio mathematica. Volume 152:Number 12(2016)
• Page Start: 2545
• Page End: 2562
• Publication Date: 2016-11-14
• Subjects: 14F05, -- 13D02 (primary); Sheaf cohomology, -- monads, -- Boij–Söderberg theory; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X16007703
• Languages: English
• ISSNs: 0010-437X

Abstract

Abstract : We use supernatural bundles to build $\mathbf{GL}$ -equivariant resolutions supported on the diagonal of $\mathbb{P}^{n}\times \mathbb{P}^{n}$, in a way that extends Beilinson's resolution of the diagonal. We thus obtain results about supernatural bundles that largely parallel known results about exceptional collections. We apply this construction to Boij–Söderberg decompositions of cohomology tables of vector bundles, yielding a proof of concept for the idea that those positive rational decompositions should admit meaningful categorifications.