A (--86)-Sphere in the K3 Surface

Authors: Sergey FINASHIN, Grigory MIKHALKIN

Abstract: Consider the self-intersection number [\Sigma].[\Sigma] of a 2-dimensional sphere \Sigma embedded into a K3 surface. Since a K3 surface is spin, [\Sigma].[\Sigma] is even and by Gauge theoretical arguments [\Sigma].[\Sigma]\le 0. No other restriction on [\Sigma].[\Sigma] is known. It is a problem 4.105(D) from the Kirby list \cite{K} to determine the possible values of [\Sigma].[\Sigma]. This paper shows that the even numbers between 0 and -86 do appear as [\Sigma].[\Sigma].

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