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arXiv · 1506.07558

Supernatural analogues of Beilinson monads

Daniel Erman·Steven V Sam
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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.

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Daniel Erman, Steven V Sam. 2015-06-24. Supernatural analogues of Beilinson monads. https://doi.org/10.1112/s0010437x16007703

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