Timeline for Desingularization of subvariety
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 13, 2016 at 20:53 | comment | added | Edward Teach | Adel, if you wich to post this as an answer, I will accept it. | |
| Sep 13, 2016 at 19:20 | comment | added | Edward Teach | Sándor, now I can find it:) Sasha, thank you. | |
| Sep 11, 2016 at 22:51 | comment | added | Adel BETINA | Hironaka proved that the strong desingularization always exists for varieties of characteristic 0, but for varieties of characteristic p, this problem stills open in dimensions 4 or more and the construction of Hironaka was improved and actually we know that the construction of $Y′$ is functorial for smooth morphisms to $Y$ and embeddings of $Y$ into a larger variety and we know also that the morphism from $X′$ to $X$ does not depend on the embedding of $X$ in $Y$. | |
| Sep 11, 2016 at 22:48 | comment | added | Adel BETINA | The construction of $Y′$ is given by a succession of a blowing up of regular closed subvarieties of $Y$ or more strongly regular subvarieties of $X$, transverse to the exceptional locus of the previous blowings up. | |
| Sep 11, 2016 at 22:48 | comment | added | Adel BETINA | If there is an embedding of X into a regular variety Y. A strong desingularization of X a proper birational morphism from a regular variety $f:Y' \rightarrow Y$ satisfying the following conditions : 1) The transform $X′$ of $X$ is regular and transverse to the exceptional locus of the resolution morphism. 2)The restriction $f_{X'}:X' \rightarrow X$ is an isomorphism away from the singular points of X (thus they have the same function field). | |
| Sep 11, 2016 at 19:21 | comment | added | Sándor Kovács | I don't know who that author is whom Sasha mentions ... :), but there is a very good book on the subject written by Kollár(!): press.princeton.edu/titles/8449.html | |
| Sep 11, 2016 at 17:04 | comment | added | Sasha | This is called "embedded resolution of singularities". A good reference is Kollar's book. | |
| Sep 11, 2016 at 16:43 | history | asked | Edward Teach | CC BY-SA 3.0 |