Timeline for Intersection multiplicty and global sections
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 24, 2015 at 5:35 | comment | added | Allen Knutson | Non-example: Let $V$ be a union of two planes at a point inside $\mathbb P^4$ (so not C-M), and $W$ a plane going through that point. Then the intersection multiplicity is of course $2$, but the scheme-theoretic intersection is a fat point of length $3$. To see the problem, let $W = W_1 \cap W_2$ be an intersection of hyperplanes. Then $V\cap W_1$ is a union of two lines and an embedded point, and $(V\cap W_1)\cap W_2$ has a point for each line (that's good) and also the embedded point (that's bad, and in particular, not transverse). | |
| Feb 23, 2015 at 22:10 | vote | accept | Kali | ||
| Feb 23, 2015 at 22:10 | comment | added | Kali | Thank you very much. This is exactly the setting I am interested in. | |
| Feb 23, 2015 at 20:59 | history | answered | Sasha | CC BY-SA 3.0 |