Timeline for A basic question on the definition of Cartan-Remmert reduction and holomorphic convexity
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 9, 2011 at 20:37 | vote | accept | aglearner | ||
| Jun 12, 2011 at 23:43 | comment | added | aglearner | mrw, thanks, I just wanted to confirm. | |
| Jun 12, 2011 at 19:12 | comment | added | mrw | Was there a problem with my answer above? Assume that $\pi:X\to Y$ if proper, surjective and has connected fibers. Then any holomorphic function on each fiber is constant. Therefore $\pi_*\mathcal O_X=\mathcal O_Y$. Viceversa, assume that $\pi_*\mathcal O_X=\mathcal O_Y$ and let $f:X\to Z$ and $g:Z\to Y$ the Stein factorization. Then $f_*\mathcal O_Z=\mathcal O_Z$ but $g_*\mathcal O_Z=\mathcal O_Y$ only if $g$ is an isomorphism, otherwise $g_*\mathcal O_Z$ would have rank greater than $1$. | |
| Jun 11, 2011 at 21:44 | comment | added | aglearner | Sylvain, thanks! This answers indeed my first question. What about the second one? | |
| Jun 11, 2011 at 1:43 | history | answered | Sylvain Bonnot | CC BY-SA 3.0 |