Timeline for Normal Varieties
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Aug 29, 2010 at 21:15 | comment | added | BCnrd | Dear Angelo: can we really bypass invoking the Riemann Extension Theorem for bounded analytic functions on normal analytic spaces? It's only the bounded analytic functions that extend, not all of them, so how can local cohomology or other purely algebraic methods detect this? I am very interested to hear the idea behind how such an argument might go. (Note: I've never really looked into gap sheaves, if that is somehow relevant.) If there is an "algebraic" proof of the Extension Theorem, I'd be happy to see that too. | |
| Aug 29, 2010 at 18:02 | comment | added | Donu Arapura | Given Keerti's answer + comments by Angelo & BCnrd, I think I'm off the hook :) | |
| Aug 29, 2010 at 17:47 | comment | added | Angelo | In fact, Keerthi Madapusi's idea works for the topological fundamental group. The point is that the statement holds for analytic spaces; by considering the universal cover, which is again an analytic space, it reduces to the statement that removing an analytic subspace of codimension 2 from a normal analytic space does not disconnect it, which follows easily from the Serre's characterization of normal local rings, by using local cohomology. | |
| Aug 29, 2010 at 15:49 | history | answered | Keerthi Madapusi | CC BY-SA 2.5 |