Rational Curves on Fibered Calabi-Yau Manifolds
Simone DiverioDipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy
Claudio FontanariDipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14 38123 Povo, Trento, Italy
Diletta MartinelliSchool of Mathematics, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh SW7 2AZ, UK
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.
Cite this article
Simone Diverio, Claudio Fontanari, Diletta Martinelli, Rational Curves on Fibered Calabi-Yau Manifolds. Doc. Math. 24 (2019), pp. 663–675DOI 10.4171/DM/691