Rational curves on fibered varieties

Fabrizio Anella

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arXiv · 1809.09454

Rational curves on fibered varieties

Fabrizio Anella

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Abstract

Let $X$ be a projective variety with log terminal singularities and vanishing augmented irregularity. In this paper we prove that if $X$ admits a relatively minimal genus one fibration then it does contain a subvariety of codimension one covered by rational curves contracted by the fibration. We then focus on the case of varieties with numerically trivial canonical bundle and we discuss several consequences of this result.

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BibTeX RIS

Fabrizio Anella. 2018-09-25. Rational curves on fibered varieties. https://arxiv.org/abs/1809.09454

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