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# ToplogyTopology of K3 as a sum of two abelian fibrations.

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# Toplogy of K3 as a sum of two abelian fibration.

Let $E$ be a blow-up of $\mathbb{P}^2$ at 9-points in the bases locus of a pencil of elliptic curves (A $T^2$ fibration over $S^2$).

K3 surfaces is obtained by removing a fiber from two copies of $E$ and gluing along the boundaries.

How do we realize 22 second homology classes of K3, in terms of 10 second homology classes of $E$. I know this is classic but I could not find a reference.