Timeline for On minimal resolution of singularities and the type of singularities
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| Oct 28, 2022 at 5:02 | review | Close votes | |||
| Nov 2, 2022 at 3:01 | |||||
| Oct 3, 2010 at 3:56 | answer | added | Sándor Kovács | timeline score: 2 | |
| Jul 1, 2010 at 13:59 | vote | accept | Amira | ||
| Jun 25, 2010 at 5:31 | answer | added | Richard Montgomery | timeline score: 2 | |
| Apr 12, 2010 at 2:53 | comment | added | Karl Schwede | Alternately, if $\pi$ is \e'tale in codimension 1, then you can show that $Y$ has rational singularities. | |
| Apr 11, 2010 at 18:30 | comment | added | Torsten Ekedahl | I think you may be thinking of the case of a finite morphism $\pi\colon X \to Y$ where $X$ is smooth. In that case the singularities of $Y$ are indeed quotient singularities. Not necessarily cyclic quotient singularities however; an $E_8$-singularity for instance is the quotient of $\mathbb C^2$ by the icosahedral group which is not cyclic. | |
| Apr 11, 2010 at 16:02 | comment | added | VA. | This is still a nonsense question. Take $Y$ = the cone over an elliptic curve, and $f:Y\to X$ a projection to $Y=\mathbb P^2$. $Y$ is normal, the singularity is not cyclic quotient. | |
| Apr 11, 2010 at 15:48 | history | edited | Amira | CC BY-SA 2.5 |
I changed the set-up a bit. It was too general and I emphasized my motivation.; deleted 1 characters in body
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| Apr 11, 2010 at 15:44 | comment | added | Amira | Ok. My question is too general. I edited it. (I'm really confused here.) Could somebody maybe give a reference to where all this material on "singularity types" is written down carefully? I'd like to understand how to show that cyclic quotient singularities are rational in my case. | |
| Apr 11, 2010 at 14:44 | comment | added | Charles Siegel | @Torsten: My thought is that Amira has something crossed from the ADE singularities. Not familiar enough with the general theory though to be sure of what. | |
| Apr 11, 2010 at 14:29 | comment | added | Torsten Ekedahl | There are many more normal surface singularities than cyclic quotient singularities or for that matter rational singularities (which is defined by the condition of the second paragraph). You must have misinterpreted something. To take just one example: The cone point of the affine cone of an elliptic curve (embedded in the projective plane say) is not a rational singularity. | |
| Apr 11, 2010 at 14:16 | history | asked | Amira | CC BY-SA 2.5 |