Timeline for Intersection Cohomology of Coordinate Hyperplanes
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 28, 2010 at 17:00 | vote | accept | Dinakar Muthiah | ||
| Nov 28, 2010 at 16:44 | comment | added | Mike Skirvin | One further comment: On an irreducible variety, IC sheaves are indecomposable in the derived category, as stated in Corollary 2 of section 4.1 of "Intersection Homology II." This would certainly seem to be a good reason for usually dealing with irreducible varieties. | |
| Nov 28, 2010 at 16:36 | comment | added | Mike Skirvin | Jan, that's certainly a good point to bring up. I think they assume irreducible throughout because it makes things less messy and I think it's necessary for the decomposition theorem. However, if you look at Goresky and MacPherson's "Intersection Homology II," you'll see that the IC sheaf can be defined for a fairly large class of topological spaces known as pseudomanifolds (maybe you knew this already) and there is still a uniqueness result like the one you ask for (see 4.1 and 6.1 of "Intersection Homology II"). In the OP's question, $X$ is pure dimensional which means we should be ok. | |
| Nov 28, 2010 at 8:36 | comment | added | Jan Weidner | A small detail, which makes me nervous: In "D-modules, perverse sheaves and Representation theory", they don't even define IC-complexes on non irreducible varieties. Given a not necessarily irreducible variety with equidimensional components. Is there still a unique complex which coincides on a dense open subset with a given shifted local system, and satisfies the (co)support condition for IC complexes? | |
| Nov 28, 2010 at 6:33 | history | edited | Mike Skirvin | CC BY-SA 2.5 |
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| Nov 27, 2010 at 18:35 | comment | added | Dinakar Muthiah | Can you elaborate on the argument in part 1? I'm sorry to belabor it, but I think I need it spelled out to me. | |
| Nov 27, 2010 at 17:55 | history | answered | Mike Skirvin | CC BY-SA 2.5 |