Frobenius pushforwards on Grassmannians Gr(2,n)
Theo Raedschelders (University of Glasgow)
Wednesday 10th January, 2018 16:00-17:00 Maths 116
In this talk I will introduce the notion of a tilting bundle on a smooth projective variety and we will see how such bundles can be constructed on Grassmannians using representations of the general linear group. In positive characteristic there was some hope that tilting bundles could be canonically obtained from the Frobenius morphism, but this sadly turns out not to be the case. I will discuss recent results with Špela Špenko and Michel Van den Bergh which allow for a detailed description of what goes wrong for Grassmannians of 2-dimensional quotients. If time permits, I will also describe some positive results related to the existence of noncommutative resolutions.