Timeline for Normal Macaulayfications
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 17, 2021 at 20:33 | answer | added | macaulayfication411 | timeline score: 0 | |
| Nov 29, 2014 at 18:52 | comment | added | user62384 | As a related question, has there been any result as to whether Kawasaki's Macaulayfication can be taken to be an isomorphism over the CM locus? I think he shows that a finite set of CM points can be taken in the isomorphism locus but that he does not say anything about this other problem. | |
| Apr 2, 2013 at 20:01 | comment | added | Jason Starr | I double-checked about alterations. Unfortunately, one first has to allow for a projective, dominant, generically finite morphism $X'\to X$ whose extension of fraction fields is purely inseparable. Then one has $Y\to X'$ and $G$ as above. | |
| Apr 2, 2013 at 17:35 | comment | added | Jason Starr | Have you looked at Gabber's formulation of de Jong's alterations? My impression is that for a given $X$ (perhaps quasi-projective over a field), there exists a proper, birational modification which is of the form $Y/G$ where $Y$ is a regular scheme and where $G$ is a finite (reduced) group acting on $Y$ generically freely. If $G$ had order prime to the characteristic, then $Y/G$ would be Cohen-Macaulay. A good person to ask would be Chenyang Xu -- he and Esnault used this technique to say something about point counts over finite fields. | |
| Apr 1, 2013 at 16:02 | answer | added | Alberto F. Boix | timeline score: 3 | |
| Dec 9, 2010 at 15:18 | comment | added | Karl Schwede | Sandor, it might be possible, but I don't see why it would work off the top of my head. There has been some work on Macaulayfications since Kawasaki's result, and I was hoping that maybe there is some stuff since then that implies something along these lines in a way that someone here might know but that I didn't realize. However, overall I agree, and I also guess that this is question is probably quite hard. | |
| Dec 9, 2010 at 5:06 | comment | added | Sándor Kovács | Karl, is it possible to start with the normalization, then apply normalized blow ups and try to prove that this way one also gets a CM-ification as in Kawasaki's paper? I realize this is a shot in a very dark space with no reasonable comments to back it up, but the point is that my feeling is that this will not have an easy answer that would be fitting for a question/answer on MO. I would expect that this requires some serious work. | |
| Dec 8, 2010 at 18:10 | history | asked | Karl Schwede | CC BY-SA 2.5 |