Timeline for Comparing fundamental groups of a complex orbifolds and their resolutions.
Current License: CC BY-SA 2.5
6 events
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| Dec 29, 2010 at 21:17 | comment | added | Francesco Polizzi | dimitri, you are right, my argument using armstrong result only proves that if G=E then there exists a neighborhood of the singularity which is simply connected, but it says nothing about the resolution... | |
| Dec 29, 2010 at 14:15 | comment | added | Dmitri Panov | Francesco, sorry, I try to understand what you say. I just have not got what is conclusion of the second part of the answer... (starting form the result of Armstrong) | |
| Dec 29, 2010 at 13:53 | comment | added | Francesco Polizzi | Dimitri, I just meant that locally analitically a quotient singularity is of the form $\mathbb{C}^n/G$, where $G \subset \textrm{Aut}(\mathbb{C}^n)$. So if for every singular point you know the local $G$-action and you are able to verify that $G=E$, then it seems to me that you can apply the usual Seifert-Van Kampen argument to conclude... | |
| Dec 29, 2010 at 13:22 | comment | added | Dmitri Panov | Francesco, thanks a lot for your detailed answer! I'll have a look on the result of Fujiki. I do believe that the statement is always true, for example because the result of Fujiki should hold not only for isolated cyclic quotient singularities. (Though, if BCPG only have a reference to this result, maybe it is the best one written down... :( ). I have not quite got what you mean when you say that in my case $V=\mathbb C^n$ ... (maybe I have not formulated my question properly, but my question is about Any complex manifold with quotient singularities). | |
| Dec 29, 2010 at 9:49 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
added 79 characters in body
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| Dec 29, 2010 at 9:38 | history | answered | Francesco Polizzi | CC BY-SA 2.5 |