Speaker: Frank Gounelas, TU Munich
Time: Monday 28th September 4 to 5pm (joining time 3.50pm IST)
Google Meet Link:
https://meet.google.com/qvo-kduy-yco
Title: Curves on K3 surfaces
Abstract: I will survey the recent completion (joint with Chen-Liedtke) of
the remaining cases of the conjecture that a projective K3 surface
contains infinitely many rational curves. As a consequence of this along
with the Bogomolov-Miyaoka-Yau inequality and the deformation theory of
stable maps, I will explain (joint with Chen) how in characteristic zero
one can deduce the existence of infinitely many curves of any geometric
genus moving in maximal moduli on a K3 surface. In particular this leads
to an algebraic proof of a theorem of Kobayashi on vanishing of global
symmetric differentials and applications to 0-cycles.