Timeline for How to determine "genericness" of an element of a family of algebraic varieties?
Current License: CC BY-SA 3.0
8 events
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| Jun 4, 2013 at 13:32 | history | edited | pinaki | CC BY-SA 3.0 |
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| Jun 4, 2013 at 2:34 | answer | added | Donu Arapura | timeline score: 1 | |
| Jun 3, 2013 at 23:25 | comment | added | Qfwfq | If $\mathcal{X}\to C$ is a smooth morphism, then under your hypothesis (projectiveness) a theorem of Ehresmann assures the fibers are all diffeomorphic. | |
| Jun 3, 2013 at 23:03 | comment | added | Will Sawin | I'm not sure which conditions are needed to make this true. | |
| Jun 3, 2013 at 23:03 | comment | added | Will Sawin | I'm guessing the best cohomological way to detect genericity is going to be the vanishing cycle sheaf. You want a statement like: If there are no vanishing cycles, the fiber is homeomorphic to generic $X_t$. | |
| Jun 3, 2013 at 22:36 | history | edited | pinaki | CC BY-SA 3.0 |
added 340 characters in body
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| Jun 3, 2013 at 21:38 | comment | added | IMeasy | I think A true, B false. But for now I have no time to detail this. I'll come back soon! | |
| Jun 3, 2013 at 20:36 | history | asked | pinaki | CC BY-SA 3.0 |