Speaker: Sergey Galkin

Title: Acyclic line bundles on fake projective planes

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

Place: HSE, Room 1001

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.