Rational curves on fibered Calabi-Yau manifolds

31 Aug 2018 Diverio Simone Fontanari Claudio Martinelli Diletta

We show that a smooth projective complex manifold of dimension greater than two endowed with an elliptic fiber space structure and with finite fundamental group always contains a rational curve, provided its canonical bundle is relatively trivial. As an application of this result, we prove that any Calabi-Yau manifold that admits a fibration onto a curve whose general fibers are abelian varieties always contains a rational curve...

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