Geodesic
Rational Curves on Fibered Calabi-Yau Manifolds
Documenta mathematica, Tome 24 (2019), pp. 663-675
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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.
DOI : 10.4171/dm/691
Classification : 14E30, 14J32, 32Q55
Mots-clés : fibration, Calabi-Yau manifold, elliptic fiber space, rational curve, rational multi-section, canonical bundle formula 
@article{10_4171_dm_691,
     author = {Simone Diverio and Diletta Martinelli and Claudio Fontanari},
     title = {Rational {Curves} on {Fibered} {Calabi-Yau} {Manifolds}},
     journal = {Documenta mathematica},
     pages = {663--675},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/691},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/691/}
}
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Simone Diverio; Diletta Martinelli; Claudio Fontanari. Rational Curves on Fibered Calabi-Yau Manifolds. Documenta mathematica, Tome 24 (2019), pp. 663-675. doi: 10.4171/dm/691

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