Timeline for Jacobian criterion for smoothness of schemes
Current License: CC BY-SA 3.0
5 events
when toggle format | what | by | license | comment | |
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May 14, 2018 at 3:36 | comment | added | Ashvin Swaminathan | Qing Liu's proof is great, but I think you can prove this without any algebraic geometry. If you add a "useless" generator $f_{n+1}$ to the given list, then the corresponding row of the Jacobian is a linear combination of the other rows, so adding such "useless" generators doesn't change the rank. Thus, if $f_{r+1}, \dots, f_n$ and $g_{r+1}, \dots, g_m$ are two different lists of generators, the associated Jacobians have the same rank as the Jacobian associated to the combined list $f_{r+1}, \dots, f_n, g_{r+1}, \dots, g_m$. | |
Nov 3, 2011 at 23:27 | vote | accept | Nicolás | ||
Nov 3, 2011 at 20:56 | answer | added | Qing Liu | timeline score: 13 | |
Nov 3, 2011 at 18:19 | answer | added | Greg Muller | timeline score: 3 | |
Nov 3, 2011 at 18:09 | history | asked | Nicolás | CC BY-SA 3.0 |