Timeline for Intersection product when one factor is contained in the exceptional divisor
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 26, 2021 at 20:56 | comment | added | Galathea | Thank you! Out of interest though, are there any cases when it is not ok to use the projection formula? | |
| Apr 26, 2021 at 16:47 | comment | added | Tabes Bridges | @Gala just as you indicated in your post: $\varphi_*(\varphi^* D.\alpha) = D.\varphi_*\alpha = D.0 = 0$. | |
| Apr 25, 2021 at 21:37 | comment | added | Will Sawin | If it's an intersection number, and not a class that you're after, you can use the projection formula. | |
| Apr 25, 2021 at 19:57 | comment | added | Galathea | I'm sorry, I dont understand yet. How can I use $\varphi_* \alpha = 0$ to calculate $\varphi^* D . \alpha$? I'm aware it must be simple but I do not see it.. | |
| Apr 25, 2021 at 19:52 | comment | added | abx | Because already $\varphi _*\alpha =0$, by the very definition of $\varphi _*$. | |
| Apr 25, 2021 at 19:44 | history | edited | Galathea | CC BY-SA 4.0 |
added 72 characters in body
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| Apr 25, 2021 at 19:40 | comment | added | Galathea | You are right, I was trying to make the question general, even though I am interested in the case where $dim(\varphi_* \alpha)< dim( \alpha)$. I will change the question. Can you explain though why the product would be zero in this case? It was my guess but I can't really prove it | |
| Apr 25, 2021 at 18:53 | comment | added | abx | Why would $\varphi _*(\alpha )$ have lower dimension that $\alpha $? This depends very much on the situation. If it is, it just means that the product is $0$. | |
| Apr 25, 2021 at 18:16 | review | Close votes | |||
| May 11, 2021 at 3:06 | |||||
| Apr 25, 2021 at 17:55 | review | First posts | |||
| Apr 25, 2021 at 18:12 | |||||
| Apr 25, 2021 at 17:53 | history | asked | Galathea | CC BY-SA 4.0 |