Timeline for Obtaining non-normal varieties by pushout
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Nov 10, 2014 at 12:14 | vote | accept | Qfwfq | ||
| Nov 9, 2014 at 20:23 | answer | added | Karl Schwede | timeline score: 16 | |
| Nov 7, 2014 at 1:18 | comment | added | Piotr Achinger | I think the claim above could follow from some results in Artin's paper "Algebraization of Formal Moduli II", where instead of $Z_n$ we consider their limit (the formal completion). The trick seems to be to choose an appropriate $n\gg 0$. | |
| Nov 7, 2014 at 1:16 | comment | added | Piotr Achinger | Just a comment. One might hope for the following: given a variety $X$ and a proper birational $f:X'\to X$, let $Z\subseteq X$ be the locus where $f$ is not a local isomorphism (with reduced subscheme structure). For $n\geq 1$, let $Z_n$ denote the $n$-th infinitesimal thickening of $Z$ in $X$. Then for $n\gg 0$, $X$ is the pushout of $Z_n \leftarrow f^{-1}(Z_n)\to X'$. To answer your question, we would apply this to the normalization map (as hinted by Karl Schwede). | |
| Nov 6, 2014 at 20:38 | history | asked | Qfwfq | CC BY-SA 3.0 |