Timeline for Is the Gysin pullback of an effective cycle effective?
Current License: CC BY-SA 3.0
4 events
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| Oct 12, 2015 at 21:58 | comment | added | Allen Knutson | Don't you want to end up in $A_k(X)$? If I'm not misreading, then consider $E = \mathcal O(-1)$ over $X = \mathbb P^1$, and $a=[$the zero section$]$. | |
| Oct 12, 2015 at 16:17 | comment | added | Jason Starr | "nonzero" --> "non-effective". Sorry for the typo. | |
| Oct 12, 2015 at 15:19 | comment | added | Jason Starr | Since Gysin pullback for the zero section is, by definition, the inverse of the flat pullback isomorphism, you can phrase your question in terms of whether flat pullback of a non-effective cycle may be effective. Indeed it may: for a rank $1$ vector bundle $E\to X$ whose first Chern class is nonzero, nonetheless the image of the zero section is an effective cycle on $E$ that is rationally equivalent to the pullback of the first Chern class. | |
| Oct 12, 2015 at 14:30 | history | asked | user39380 | CC BY-SA 3.0 |