Timeline for Zariski Connectedness Theorem in Complex Geometry
Current License: CC BY-SA 4.0
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| Sep 24 at 8:28 | comment | added | user267839 | Eg, did he always for formulating his "priciple of degeneration" assumed $X$ to be projective? (almost sure, yes) That the linear systems he considered are base point free? | |
| Sep 24 at 8:27 | comment | added | user267839 | ...although, the statement in quoted book is phrased in terms of correspondences, so it seems to be phrased more in Zariski's "style" terms from his Theory and applications of holomorphic functions as so far I know Enriques worked instead with linear systems, so in modern terms about maps $X -(\text{Base Loc of L}) \to \Bbb P^n$ induced by linear systems $L$. The question then would be what Enriques tacitly made as basic assumtions. | |
| Sep 24 at 8:13 | comment | added | user267839 | @PiotrAchinger: Thanks, indeed Stein's factozization was originally stated in complex setting; let me add this (complex setting adressing intuition on Stein decomp) and this (on "general intuition") discussions appeared very helpful. Actually I think Enriques reasoned originally similar as in proof of ZCT (3.24), p 52 in Mumford's AG I, Complex Alebraic Varieties, see esp. the marked footnote | |
| Sep 23 at 20:54 | comment | added | Piotr Achinger | There must be a reason why Stein factorization is named after Stein... | |
| Sep 23 at 20:07 | history | edited | user267839 | CC BY-SA 4.0 |
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| Sep 23 at 18:04 | history | edited | user267839 | CC BY-SA 4.0 |
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| Sep 23 at 17:53 | history | edited | user267839 | CC BY-SA 4.0 |
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| Sep 23 at 17:45 | history | edited | user267839 | CC BY-SA 4.0 |
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| Sep 23 at 17:38 | history | asked | user267839 | CC BY-SA 4.0 |