Timeline for Relation between Castelnuovo-Mumford regularity for coherent sheaves and modules
Current License: CC BY-SA 3.0
10 events
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| Sep 18, 2013 at 4:28 | comment | added | Fred Rohrer | Dear @Chen, you might also want to have a look at section 20.4 in M. Brodmann, R.Y. Sharp, Local cohomology (Cambridge studies in advanced mathematics 136). | |
| Sep 17, 2013 at 21:36 | history | edited | Chen | CC BY-SA 3.0 |
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| Sep 17, 2013 at 18:37 | comment | added | Chen | @Starr: I have edited the question | |
| Sep 17, 2013 at 17:57 | history | edited | Chen | CC BY-SA 3.0 |
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| Sep 17, 2013 at 17:15 | comment | added | Jason Starr | I am not sure that these are precisely the same. What if $X$ is disconnected? The global sections of twists of $\mathcal{O}_X(-C)$ might be a little bigger than the corresponding graded pieces of $I_C/I_X$. | |
| Sep 17, 2013 at 16:58 | comment | added | Karl Schwede | Mel Hochster has some notes on local cohomology which do this in detail, but these are not freely available online. Various papers of Karen Smith also explain this in a lot of detail. Have you looked at any of her survey papers from the 90s? Finally, the relation between graded local cohomology and coherent cohomology is pretty easy to see if you consider Cech-cohomology. | |
| Sep 17, 2013 at 16:56 | comment | added | Chen | @Schwede: It would be very helpful if you could cite some reference please. | |
| Sep 17, 2013 at 16:54 | comment | added | Chen | @Schwede: That was the question. I could not find it mentioned in any literature. | |
| Sep 17, 2013 at 16:53 | comment | added | Karl Schwede | Aren't they the same? You can compute the regularity of $I_C/I_X$ via local cohomology, the graded pieces are coherent cohomology of $O_X(-C)$, right? | |
| Sep 17, 2013 at 16:44 | history | asked | Chen | CC BY-SA 3.0 |