Algebraic Geometry Seminar
Alex Kuronya
Budapest University of Technology and Economics
Kodaira vanishing for q-ample divisors
Abstract: Line bundles sharing some but not all the good properties of
ampleness have been investigated for quite some time, here we will focus on
the cohomological point of view. Building on earlier work of Sommese and
Demailly-Peternell-Schneider, Totaro came up with a very satisfactory theory
of line bundles with partially vanishing higher cohomology to which we will
refer as q-ample.
As it turns out, q-ampleness gives rise to interesting applications,
including a useful concept of ampleness for subvarieties, where among others,
one retains a Lefschetz hyperplane theorem (as showed by Ottem).
The main focus of this talk will be a generalization of Kodaira vanishing
to q-ample line bundles.
Wednesday October 22, 2014 at 4:00 PM in SEO 427