Timeline for A question on the effective cone
Current License: CC BY-SA 3.0
5 events
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| Feb 24, 2015 at 17:05 | comment | added | user47305 | You could try $Y$ the blow-up of $\mathbb P^2$ at $4 \leq k \leq 8$ points, and $X$ the double-cover branched over a conic missing all the points. Certainly $Y$ has polyhedral cone, but $X$ is $\mathbb P^1 \times \mathbb P^1$ blown up at $2k$ points, which is isomorphic to $\mathbb P^2$ blown up at $2k+1$ points. My guess is that $X$ can have infinitely many rays, but there's something to check since the resulting $2k+1$ points aren't general. For $k=8$ I think it's easy to see this works, though I'm not sure about $k=4$. | |
| Feb 24, 2015 at 16:09 | comment | added | user68440 | Thanks! Do you have an example with $Pic(X)$ finitely generated? | |
| Feb 24, 2015 at 3:03 | history | edited | user47305 | CC BY-SA 3.0 |
maybe it's true.
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| Feb 24, 2015 at 2:54 | history | edited | user47305 | CC BY-SA 3.0 |
deleted 2 characters in body
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| Feb 24, 2015 at 2:49 | history | answered | user47305 | CC BY-SA 3.0 |