Abstract

We study sections of a Calabi-Yau threefold fibered over a curve by K3 surfaces. We show that there exist infinitely many isolated sections on certain K3 fibered Calabi-Yau threefolds and that the group of algebraic 1 1 -cycles generated by these sections modulo algebraic equivalence is not finitely generated. We also give examples of K 3 3 surfaces over the function field F F of a complex curve with Zariski dense F F -rational points, whose geometric model is Calabi-Yau.

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