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.
Rational curves on fibered Calabi-Yau manifolds / Diverio, Simone; Fontanari, Claudio; Martinelli, Diletta. - In: DOCUMENTA MATHEMATICA. - ISSN 1431-0635. - 24:(2019), pp. 663-675. [10.25537/dm.2019v24.663-675]
Rational curves on fibered Calabi-Yau manifolds
Fontanari, Claudio;Martinelli, Diletta
2019-01-01
Abstract
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.File | Dimensione | Formato | |
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