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, S; Fontanari, C; Martinelli, D. - In: DOCUMENTA MATHEMATICA. - ISSN 1431-0643. - 24:(2019), pp. 663-675.
RATIONAL CURVES ON FIBERED CALABI-YAU MANIFOLDS
Diverio, S
Membro del Collaboration Group
;
2019
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 allegati a questo prodotto
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