In 1964, Horrocks proved that a vector bundle on a projective space splits as a sum of line bundles if and only if it has no intermediate cohomology. Then in 2015, Eisenbud-Erman-Schreyer used the BGG correspondence for products of projective spaces to prove a version of this criterion under an additional hypothesis. This talk is about the key ingredient for proving a Horrocks-type splitting criterion for vector bundles over a smooth projective toric variety X of Picard rank 2: a short resolution of the diagonal sheaf consisting of finite direct sums of line bundles. I'll discuss the motivations and techniques and explain construction via a variant of Weyman's "geometric technique." This is joint work with Michael Brown.

The talk will be virtual, but we will have a watch party in our usual room. If you would like the zoom info to attend virtually instead, email an organizer or join our mailing list.