Rational curves on fibered Calabi-Yau manifolds
Algebraic Geometry
2018-09-10 v3
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 fibers are abelian varieties always contains a rational curve.
Keywords
Cite
@article{arxiv.1607.01561,
title = {Rational curves on fibered Calabi-Yau manifolds},
author = {Simone Diverio and Claudio Fontanari and Diletta Martinelli},
journal= {arXiv preprint arXiv:1607.01561},
year = {2018}
}