Gluing construction of K3 surfaces and Arnol'd's type theorems on a neighborhood of a curve

2018/05/25 Fri 10:30 - 12:00
Room 152, Building No.3
Takayuki Koike
Osaka City University

Arnol'd showed the uniqueness of the complex analytic structure of a small neighborhood of a non-singular elliptic curve embedded in a non-singular surface whose normal bundle satisfies Diophantine condition in the Picard variety.
As an application, we construct a K3 surface by patching two open complex surfaces obtained as the complements of tubular neighborhoods of anti-canonical divisors of the blow-ups of the projective planes at general nine points.
We also show an analogue of this Arnol'd's theorem for a neighborhood of a cycle of rational curves and consider an application of it.