Timeline for Stable base locus of a divisor and negative intersection with curves
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 5, 2015 at 12:44 | vote | accept | Li Yutong | ||
| Jan 5, 2015 at 6:58 | comment | added | user47305 | $X$ is not toric! You can blow up $4$ general points in $\mathbb P^3$ and get a toric variety, but no more ([1,0,0,0] etc are torus-invariant points, but that's it). However, it's still a Mori dream space for up to $7$ points, and so nef divisors are semiample. One you hit $8$, everything goes bad; it's a lot like $\mathbb P^2$ blown up at $9$ points versus $8$. | |
| Jan 5, 2015 at 6:12 | comment | added | Li Yutong | Thank you for your answer! But I did not quite follow your example: In your example, $X$ is a toric variety, hence any nef divisor is base point free (in particular $D$ is basepoint free if it is nef). Where did I understand wrong? | |
| Jan 4, 2015 at 16:20 | comment | added | user47305 | You could a little closer if you instead considered the diminished base locus $\mathbf B_-(D) = \bigcup_{\text{$A$ ample}} \mathbf B(D+A)$, which is a subset of $\mathbf B(D)$. Both are probably still false, but it's at least true that if $\mathbf B_-(D)$ is non-empty, $D$ is not nef. | |
| Jan 4, 2015 at 15:27 | history | answered | user47305 | CC BY-SA 3.0 |