Timeline for Grauert's semicontinuity theorem over the real field
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 29, 2017 at 16:13 | comment | added | Ben McKay | You didn't say you wanted the fibers to be manifolds. | |
| Jun 29, 2017 at 15:40 | comment | added | pfortuny | Yes. Sorry again, (0,...,0) is an isolated singularity of (f=0), so that fiber is not a differentiable manifold. | |
| Jun 29, 2017 at 13:57 | history | edited | Ben McKay | CC BY-SA 3.0 |
added another example
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| Jun 29, 2017 at 12:49 | comment | added | Ben McKay | If the fibers are all compact, and $f$ is a submersion, then all fibers near any given fiber are diffeomorphic, by usual argument: construct (using partition of unity) a vector field on $X$ projecting to the usual translation field on $\mathbb{R}$, and flow fibers. | |
| Jun 29, 2017 at 12:46 | history | edited | Ben McKay | CC BY-SA 3.0 |
added constant dimensional fiber case
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| Jun 29, 2017 at 11:04 | comment | added | pfortuny | Oh, sorry. This comes from thinking without examples...... Thanks. The fibers have constant dimension, in my case. But I have to look at the problem in more detail. | |
| Jun 29, 2017 at 11:03 | history | answered | Ben McKay | CC BY-SA 3.0 |