Timeline for Examples where it's useful to know that a mathematical object belongs to some family of objects
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jun 12, 2014 at 4:36 | history | edited | bananastack | CC BY-SA 3.0 |
fixed link to sard's theorem
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| Sep 1, 2011 at 11:25 | comment | added | David E Speyer | Your right that I am glossing over steps. In more (but not complete detail): $X$ is closed in $U \times \mathbb{CP}^4$ (exercise). Thus the map $X \to U$ is proper. Proper plus finite fibers means a finite map. Finite map with all fibers the same cardinality is etale (in characteristic $0$). Etale and finite is a covering map. | |
| Sep 1, 2011 at 10:42 | comment | added | Bruno Martelli | Nice. How does the fact that the fiber of $X \to U$ has constant cardinality $9^4$ imply that it is a covering? | |
| Sep 1, 2011 at 3:29 | history | edited | Charles Staats | CC BY-SA 3.0 |
added 1 characters in body
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| Sep 1, 2011 at 2:49 | comment | added | Steven Landsburg | (PS---"Exactly what I had in mind" should not be misread to mean that I had this example in mind. This is, instead, exactly the kind of thing I was looking for. | |
| Sep 1, 2011 at 2:48 | comment | added | Steven Landsburg | Terrific --- exactly what I had in mind, except perhaps for the easily-explainable to-undergraduates part. Thank you! | |
| Sep 1, 2011 at 2:34 | history | answered | David E Speyer | CC BY-SA 3.0 |