Timeline for Reference for flatness in complex-analytic geometry
Current License: CC BY-SA 3.0
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| Mar 23, 2018 at 16:33 | vote | accept | CommunityBot | ||
| Mar 10, 2018 at 7:40 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Mar 10, 2018 at 7:26 | answer | added | Francesco Polizzi | timeline score: 9 | |
| Mar 10, 2018 at 3:53 | comment | added | nfdc23 | The key is that a non-empty complex-analytic space admits points that are Cohen-Macaulay (work locally, using finite maps to a ball of suitable dimension as in the setup of dimension theory in the G-R book). For a flat map and a CM point in a fiber one can make a "locally quasi-finite quasi-section" adapting the slicing argument as in the scheme case. But for a map of complex-analytic spaces, near an isolated point in a fiber it is finite after shrinking on source and target. Thus, locally on the base there exists a finite flat quasi-section. Then openness and coherent descent are clear. | |
| Mar 10, 2018 at 3:29 | history | edited | user95222 | CC BY-SA 3.0 |
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| Mar 10, 2018 at 1:45 | history | edited | user95222 |
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| Mar 10, 2018 at 1:25 | history | asked | user95222 | CC BY-SA 3.0 |