Every rational Hodge isometry between two K3 surfaces is algebraic

Abstract

We prove that given any rational Hodge isometry $\psi :H^2(S_1,\mathbb{Q})\to H^2(S_2,\mathbb{Q})$ between any two Kähler $K3$ surfaces $S_1$ and $S_2$ the cohomology class of $\psi$ in $H^{2,2}(S_1\times S_2)$ is a polynomial in Chern classes of coherent analytic sheaves over $S_1\times S_2$. Consequently, the cohomology class of $\psi$ is algebraic whenever $S_1$ and $S_2$ are algebraic.

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• Vector bundles on a K3 surface
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