Timeline for Lower bound for intersection number
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2011 at 11:51 | comment | added | naf | Yes, that's right. So you could replace $\mathbf{P}^1$ by any smooth projective curve. | |
| Oct 9, 2011 at 11:29 | comment | added | Taicho | So the self-intersection of $P$ is well-defined in this case because $\mathbf{P}^1$ is proper over the base field, right? | |
| Oct 9, 2011 at 11:22 | history | edited | Taicho | CC BY-SA 3.0 |
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| Oct 9, 2011 at 11:01 | comment | added | naf | Your idea (and the statement itself) is correct only if $D$ is an effective divisor. In this case you can replace $P$ by any integral divisor. If the base is not proper then one cannot define intersection numbers for horizontal divisors. | |
| Oct 9, 2011 at 9:37 | comment | added | Taicho | $(P,P)$ is the self-intersection of $P$. So I should have denoted that by $P\cdot P$. The order of $D$ at $P$ is denoted by $\mathrm{ord}_P(D)$. | |
| Oct 9, 2011 at 9:36 | history | edited | Taicho | CC BY-SA 3.0 |
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| Oct 9, 2011 at 9:36 | comment | added | naf | What do $ord_P(D)$ and $(P,P)$ mean? | |
| Oct 9, 2011 at 8:50 | history | asked | Taicho | CC BY-SA 3.0 |