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- Title
Supernatural analogues of Beilinson monads.
- Authors
Erman, Daniel; Sam, Steven V
- 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.
- Subjects
ANALOGY; MONADS (Mathematics); COHOMOLOGY theory; VECTORS (Calculus); MATHEMATICAL analysis
- Publication
Compositio Mathematica, 2016, Vol 152, Issue 12, p2545
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X16007703