Timeline for proper mapping between Stein manifolds
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| S Aug 12, 2013 at 9:54 | history | suggested | Michael Albanese | CC BY-SA 3.0 |
Replaced \\# by \#.
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| Aug 12, 2013 at 9:52 | review | Suggested edits | |||
| S Aug 12, 2013 at 9:54 | |||||
| Jun 2, 2013 at 6:05 | comment | added | Jun Li | I'm sorry for the ambiguous.The map $b$ is in general not surjective.$X$ and $Y$ are both smooth and connected.Thank you for the comments. | |
| May 31, 2013 at 17:02 | history | edited | user9072 | CC BY-SA 3.0 |
format and tags
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| May 31, 2013 at 15:09 | comment | added | user30180 | If $X$ is connected and $b$ is surjective then $X$ and $Y$ have the same dimension at all points, so $b$ is necessarily flat (in the sense of maps of local rings), so the coherent sheaf $b_{\ast}(O_X)$ is a vector bundle on $Y$. The rank of this vector bundle must be constant since $Y$ is connected, and it provides a uniform upper bound on the size of fibers. Are you interested in cases with either $X$ disconnected or $b$ not surjective? | |
| May 31, 2013 at 14:48 | comment | added | user30180 | You must be assuming $Y$ is connected. Are you assuming $X$ is connected or $b$ is surjective? It is false without at least one of those, so please state all of your hypotheses. | |
| May 31, 2013 at 13:16 | history | asked | Jun Li | CC BY-SA 3.0 |