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Questions about K3 surfaces, which are smooth complex surfaces $X$ with trivial canonical bundle and vanishing $H^1(O_X)$. They are examples of Calabi-Yau varieties of dimension $2$.

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Algebraic cycles on a K3 surface after hyperKahler rotation.

I admit that this seems a little surprising, but I don't see the contradiction. You have made genericity assumptions about everything except for the existence of a lattice polarization. A generic K3 h …
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