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For questions about the Kodaira dimension of a compact complex manifold $X$, a numerical invariant which takes value in $\{-\infty, 0, 1, \dots, \dim X\}$.

5 votes
1 answer
511 views

Properly elliptic surface with no multiple fibers and without a section

I am aware that if an elliptic surface contains multiple fibers, then it has no section. Is the converse false? In particular, I am looking for an example of a projective, properly elliptic surface …
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