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clarification of the questions
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edit approved Jul 11, 2018 at 21:09
user564401
edit approved Jul 11, 2018 at 21:09
user564401
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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 (Kodaira dimension 1), fibered over $\mathbb{P}^1$, with no multiple fibers and no 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 properly elliptic surface (Kodaira dimension 1), fibered over $\mathbb{P}^1$, with no multiple fibers and no 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 (Kodaira dimension 1), fibered over $\mathbb{P}^1$, with no multiple fibers and no section.

Source Link
user564401
user564401
  • 61
  • 5

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 properly elliptic surface (Kodaira dimension 1), fibered over $\mathbb{P}^1$, with no multiple fibers and no section.