Diverio, Simone; Fontanari, Claudio; Martinelli, Diletta

Rational Curves on Fibered Calabi-Yau Manifolds

Doc. Math. 24, 663-675 (2019)
DOI: 10.25537/dm.2019v24.663-675
Communicated by Gavril Farkas

Summary

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.

Mathematics Subject Classification

14J32, 32Q55, 14E30

Keywords/Phrases

elliptic fiber space, Calabi-Yau manifold, fibration, rational curve, rational multi-section, canonical bundle formula

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Affiliation

Diverio, Simone
Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy
Fontanari, Claudio
Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14 38123 Povo, Trento, Italy
Martinelli, Diletta
School of Mathematics, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh SW7 2AZ, UK

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