Takayuki Koike

In this talk, we construct K3 surfaces by gluing two rational surfaces
given by blowing-up the projective plane at "general" nine points. For
such K3 surfaces, one can concretely calculate the period maps. By
observing the result of this calculation, one can show that such K3
surfaces constitute a large family which includes non-projective K3
surfaces as general elements. This gluing construction is based on
Arnol'd's theorem on the existence of nice neighborhoods of an
elliptic curve embedded in a surface whose normal bundle satisfies
Diophantine-type condition in the Picard variety. This is a joint work
in progress with T. Uehara.