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arXiv · 1809.09485

Rational curves on genus one fibrations

Fabrizio Anella
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Abstract

In this paper we look for necessary and sufficient conditions for a genus one fibration to have rational curves. We show that a projective variety with log terminal singularities that admits a relatively minimal genus one fibration $X\rightarrow B$ does contain vertical rational curves if and only if it not isomorphic to a finite \'etale quotient of a product $\tilde{B}\times E$ over $B$. Many sufficient conditions for the existence of rational curves in a variety that admits a genus one fibration are proved in this paper.

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Fabrizio Anella. 2018-09-25. Rational curves on genus one fibrations. https://arxiv.org/abs/1809.09485

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