Timeline for Affine bundles over varieties
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 8, 2011 at 5:46 | vote | accept | rvk | ||
| Feb 7, 2011 at 0:53 | comment | added | Georges Elencwajg | Dear Dave, no, no, I'm with you , AByer and David on prefering (2) and that is what I mean with my notation $Aff_n(k)$ . I'm sorry that my post was ambiguous on this point : I've just edited it and adopted your excellent terminology "affine-linear". It is amusing that you mention Fulton: his meaning (1) for "affine bundle" had also struck me as unusual, but on the other hand it makes more general his surjectivity theorem for the morphism of Chow groups induced by the projection of an affine bundle . | |
| Feb 6, 2011 at 19:16 | comment | added | Dave Anderson | I prefer (2) as well, but Fulton's Intersection Theory uses (1) -- and it seems others (e.g. Georges!) do as well. | |
| Feb 6, 2011 at 14:39 | comment | added | David E Speyer | I agree with AByer on common usage. The other useful test is that, given a vector bundle $V$, the torsors for $V$ are classified by $H^1(X, V)$. For example (exercise!), in the $\mathbb{P}^1 \times \mathbb{P}^1$ example, the vector bundle is $\mathcal{O}(-2)$ and the affine bundle Dave gives corresponds to a nontrivial element of $H^1(X, \mathcal{O}(-2)) \cong k$. | |
| Feb 6, 2011 at 11:25 | comment | added | Arend Bayer | Just as an additional data point, I think have only seen the meaning (2). | |
| Feb 6, 2011 at 9:23 | history | answered | Dave Anderson | CC BY-SA 2.5 |