Sep 21 2020

# Algebraic Geometry Seminar: The cohomology of general tensor products of vector bundles on the projective plane, by Jack Huizenga

September 21, 2020

4:00 PM - 4:50 PM

Zoom

Chicago, IL

## Calendar

Jack Huizenga (Penn State): The cohomology of general tensor products of vector bundles on the projective plane

Using recent advances in the Minimal Model Program for moduli spaces of
sheaves on the projective plane, we compute the cohomology of the tensor
product of general semistable bundles on the projective plane. More
precisely, let V and W be two general stable bundles, and suppose the
numerical invariants of W are sufficiently divisible. We fully compute
the cohomology of the tensor product of V and W. In particular, we show
that if W is exceptional, then the tensor product of V and W has at most
one nonzero cohomology group determined by the slope and the Euler
characteristic, generalizing foundational results of Drézet, Göttsche
and Hirschowitz. We also characterize when the tensor product of V and W
is globally generated. Crucially, our computation is canonical given the
birational geometry of the moduli space, providing a roadmap for
tackling analogous problems on other surfaces. This is joint work with
Izzet Coskun and John Kopper.

Izzet Coskun

Sep 23, 2020

Sep 23, 2020