Timeline for Is pushforward of an ample divisor under small birational map nef?
Current License: CC BY-SA 3.0
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Oct 13, 2014 at 12:47 | comment | added | user47305 | Well, let me just explain this for the standard flop (there is probably a more general statement, but I'm not sure what it is). We can write $p^*H_X +aE =q^* H_Y$, where $E$ is the exceptional divisor. Taking the intersection with the ruling of $E$ contracted by $q$, we get that the value $a = H_X \cdot C$. Hence $p^*H_X = q^*H_Y$ if and only if $H_X \cdot C = 0$ (which can happen if $H_X$ is nef, but not if it's ample). | |
| Oct 13, 2014 at 2:08 | comment | added | Li Yutong | Dear Mark: Thank you for your answer, I understand it now. My I ask one more question: could you explain more about "$p^*H_X = q^*H_Y $ holds for a nef one only if $H_X$ is 0 on the flopping curve"? | |
| Oct 13, 2014 at 2:01 | vote | accept | Li Yutong | ||
| Oct 12, 2014 at 18:27 | history | edited | user47305 | CC BY-SA 3.0 |
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| Oct 12, 2014 at 18:21 | history | edited | user47305 | CC BY-SA 3.0 |
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| Oct 12, 2014 at 18:13 | history | answered | user47305 | CC BY-SA 3.0 |