Timeline for Optimal definition of "paving by affine spaces"?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Nov 11, 2014 at 18:25 | answer | added | Vivek Shende | timeline score: 9 | |
| Nov 11, 2014 at 17:07 | comment | added | Jim Humphreys | @Donu: Thanks for the reference. I thought I had seen this variant somewhere but couldn't recall exactly. Fulton does give it a new name, though the transition from variety to scheme probably isn't significant here. Broader definitions may be more flexible, but do they still carry all the consequences of the earlier ones? I'm also unsure what natural examples are covered by a broader version that aren't already covered by a narrower one. | |
| Nov 11, 2014 at 15:38 | comment | added | Donu Arapura | To muddy the water further, Fulton, Intersection Theory, 1.9.1 uses an even broader definition: $X_i-X_{i-1}$ is a union of affine spaces of possibly varying dimensions. He refers to this as 'a scheme with a "cellular decomposition"'. He goes on to establish some desirable properties, such as the Chow group maps onto homology with a basis given by closures of the affine spaces. I suspect that this may be sufficient for most applications. | |
| Nov 11, 2014 at 15:00 | history | asked | Jim Humphreys | CC BY-SA 3.0 |