Timeline for What does the ample cone look like?
Current License: CC BY-SA 2.5
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| Jun 6, 2010 at 23:38 | history | edited | Allen Knutson | CC BY-SA 2.5 |
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| Jun 6, 2010 at 18:02 | comment | added | damiano | An easy example is $(\mathbb{P}^1)^\rho$: it has nef cone with exactly $\rho$ extremal rays, and, if $\rho \geq 3$, it is also not a complete intersection in projective space. Moreover, any projective variety with N\'eron-Severi group of rank two has the required property. | |
| Jun 6, 2010 at 17:55 | comment | added | Gianni Bello | Forgive me, my last answer hasn't too much sense. The result on Lazarsfeld's book is true but there is no reason why it should imply the ample cone being $(\mathbf{R}+)^\rho$. It just implyes if the basis it good it contains $(\mathbf{R}+)^\rho$. I've benn too much rash. I don't know an example with the properties you're asking, I'm sorry. | |
| Jun 6, 2010 at 17:35 | history | answered | Gianni Bello | CC BY-SA 2.5 |