Supernatural analogues of Beilinson monads
Algebraic Geometry
2019-02-20 v2 Commutative Algebra
Abstract
We use supernatural bundles to build GL-equivariant resolutions supported on the diagonal of P^n x 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-S\"oderberg decompositions of cohomology tables of vector bundles, yielding a proof of concept for the idea that those positive rational decompositions should admit meaningful categorifications.
Keywords
Cite
@article{arxiv.1506.07558,
title = {Supernatural analogues of Beilinson monads},
author = {Daniel Erman and Steven V Sam},
journal= {arXiv preprint arXiv:1506.07558},
year = {2019}
}
Comments
17 pages; v2: added Prop. 4.4, expanded some proofs and corrected some typos