Timeline for Is there any holomorphic version of the tubular neighborhood theorem?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 22, 2018 at 11:13 | answer | added | Dror | timeline score: 8 | |
| Jun 14, 2017 at 17:07 | answer | added | Joey | timeline score: 14 | |
| Nov 26, 2012 at 11:21 | comment | added | Peter Dalakov | The proofs of both the differential-geometric and symplectic versions use some sort of exponential map/flow/Poincare-lemma-type argument. Heuristically, this explains why you need a very special complex manifold if you want to have a holomorphic version: you must have some sort of holomorphic exponential mapping/flow. | |
| Nov 26, 2012 at 11:15 | comment | added | Peter Dalakov | You can also look at P.Griffiths' paper "The extension problem in complex analysis", Am.J.M., Vol.88, No.2 1996 for related questions. | |
| Nov 26, 2012 at 2:44 | comment | added | Emerton | Dear jerry, You may want to look at Artin's proof of the existence of modifications in the context of algebraic spaces (discussed in his series of papers On the implicit function theorem in algebraic geometry). He proves that a modification contracting a given closed subvariety exists (as an algebraic space) provided that it exists in the formal n.h. of the subvariety. This gives an approach to Castelnuovo's theorem (and generalizations thereof) which is similar in spirit to the one you are asking about (but with complex geometry replaced by formal geometry). Regards, | |
| Nov 25, 2012 at 23:02 | answer | added | Dave Anderson | timeline score: 11 | |
| Nov 25, 2012 at 21:32 | answer | added | inkspot | timeline score: 12 | |
| Nov 25, 2012 at 14:03 | comment | added | Daniel Pomerleano | There is very nice work on etale tubular neighborhoods, beginning with Cox's thesis and which might help you with whatever problem you are considering. You can google "algebraic tubular neighborhood". | |
| Nov 25, 2012 at 12:42 | answer | added | Dmitri Panov | timeline score: 12 | |
| Nov 25, 2012 at 12:40 | answer | added | Braxton Collier | timeline score: 16 | |
| Nov 25, 2012 at 11:50 | history | asked | Yuchen Liu | CC BY-SA 3.0 |