Orateur
M.
Victor Lozovanu
(Université de Milan)
Description
In this talk I would like to present a joint work with Alex Küronya about syzygies
of ample line bundles on abelian surfaces. We study criteria for property $N_p$ , introduced in the
80’s by Green and Lazarsfeld, in terms of non-existence on the surface of elliptic curves of small
degree. The main focus of the talk is to present the main ideas of how one can tackle such
a problem, in which euclidean and convex geometry of Newton-Okounkov polygons play an
essential role. This is is due to the fact that first one can use these convex sets to describe the
local positivity properties of the line bundle and second to find effective divisors with prescribed
singularities.
