Abstract
AbstractIn 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 $$X\rightarrow B$$
X
→
B
does contain vertical rational curves if and only if it not isomorphic to a finite étale quotient of a product $$\tilde{B}\times E$$
B
~
×
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.
Funder
Università degli Studi Roma Tre
Publisher
Springer Science and Business Media LLC
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