Timeline for Zero Dimension Intersection
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 24, 2014 at 18:37 | comment | added | JYQ | Thanks a lot, Mohan and Jason. Another question, say we are working over $\mathbb{C}$, under what conditions is $s$ general enough? $s$ intersects transversally with the zero section? I think this is not enough. | |
| Jun 24, 2014 at 17:38 | comment | added | Jason Starr | Since you tagged this "algebraic topology", probably you are working over $\mathbb{C}$. I just want to point out, this type of thing can fail for smooth schemes over a finite field. If you assume that the field is infinite, then you should be able to apply Bertini theorems (probably this is what Mohan is alluding to as well). | |
| Jun 24, 2014 at 16:28 | comment | added | Mohan | Depends. $E$ may have too few sections and then $Z$ may not be even zero dimensional for any section. If $E$ is globally generated, then general section will have the property you expect. | |
| Jun 24, 2014 at 15:25 | history | edited | JYQ | CC BY-SA 3.0 |
added 57 characters in body
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| Jun 24, 2014 at 15:20 | history | asked | JYQ | CC BY-SA 3.0 |