Speaker: Sergey Galkin

Title: Acyclic line bundles on fake projective planes

Date: Nov 11, 2014, 14:00 - 15:10

Place: HSE, Room 1001

Abstract:

On a projective plane there is a unique cubic root of a canonical bundle, and it is acyclic.
On fake projective planes a cubic root of canonical bundle exists and unique if there is no 3-torsion,
and usually exists but not unique otherwise.
In 1305.4549 we conjectured that on a fake projective plane a cubic root of a canonical bundle is acyclic, if it exists.
It would suffice to prove the vanishing of global sections of a tensor square of this line bundle,
but it turned out to be very hard to prove.
I will tell about nine cases proved so far by five different methods,
including my recent work with Ilya Karzhemanov and Evgeny Shinder,
where we exploit the fact that a line bundle is _non_-linearisable to prove that it is acyclic.