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Seminar of Algebraic Geometry in East Asia
15:00 - 16:00, October 9, 2020 (Friday)
Zoom, Online seminar
(線上演講 Zoom)
Curves on K3 Surfaces
Frank Gounelas (Technische Universität München)


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 with maximal variation in 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.


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