Rational Curves on Fibered Calabi-Yau Manifolds

  • Simone Diverio

    Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy
  • Claudio Fontanari

    Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14 38123 Povo, Trento, Italy
  • Diletta Martinelli

    School of Mathematics, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh SW7 2AZ, UK
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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 fiber is an abelian variety always contains a rational curve.

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Simone Diverio, Claudio Fontanari, Diletta Martinelli, Rational Curves on Fibered Calabi-Yau Manifolds. Doc. Math. 24 (2019), pp. 663–675

DOI 10.4171/DM/691