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Timeline for Intersection in toric variety

Current License: CC BY-SA 4.0

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Jun 30 at 17:55 vote accept Robert B
Jun 30 at 17:38 history edited Will Sawin CC BY-SA 4.0
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Jun 30 at 15:36 history edited Will Sawin CC BY-SA 4.0
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Jun 30 at 15:33 comment added Will Sawin @RobertB Not if the map $W \to \mathbb P^{11}$ has two-dimensional fibers over a four-dimensional locus and $W$ is the inverse image of that locus. Being nef certainly doesn't rule that out.
Jun 30 at 15:32 comment added Robert B Thanks, you argument definitely works when $W$ is irreducible. But let us say that $W$ has a component of dimension six. In this case intersecting $W$ with 5 general sections shouldn't we see a curve in the intersection?
Jun 30 at 15:03 history answered Will Sawin CC BY-SA 4.0