Geodesic
Rational Curves on Fibered Calabi-Yau Manifolds
Documenta mathematica, Tome 24 (2019), pp. 663-675.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 14J32, 32Q55, 14E30
Keywords: elliptic fiber space, Calabi-Yau manifold, fibration, rational curve, rational multi-section, canonical bundle formula 
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     author = {Diverio, Simone and Fontanari, Claudio and Martinelli, Diletta},
     title = {Rational {Curves} on {Fibered} {Calabi-Yau} {Manifolds}},
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Diverio, Simone; Fontanari, Claudio; Martinelli, Diletta. Rational Curves on Fibered Calabi-Yau Manifolds. Documenta mathematica, Tome 24 (2019), pp. 663-675. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a44/