Timeline for The variety induced by an extension of a field
Current License: CC BY-SA 4.0
7 events
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| Sep 5, 2020 at 18:57 | comment | added | Francesco Polizzi | This is double and not bi-double, for instance because $[z_0:z_1]=[-z_0: -z_1]$ and $[-z_0:z_1]=[z_0:-z_1]$. | |
| Sep 5, 2020 at 18:50 | comment | added | Francesco Polizzi | If $k=3$ then $k-1=2$. The covering in the affine chart is clearly a bi-double cover, non tri-double. So the extension to the projective plane must be bi-double, too. Recall that $z_0$, $z_1$, $z_2$ are homogeneous coordinates. Think of the double cover given in affine coordinates by $x \mapsto x^2$: in homogeneous coordinates it becomes $[z_0 \, : \,z_1] \mapsto[z_0^2 \, : \,z_1^2]$. | |
| Sep 5, 2020 at 15:06 | comment | added | Federico Fallucca | But in this case $\pi$ would be a $(Z/2Z)^3$ covering and not a $(Z/2Z)^2$-covering, right? | |
| Aug 14, 2020 at 10:09 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
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| Aug 13, 2020 at 17:54 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
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| Aug 13, 2020 at 16:04 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
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| Aug 13, 2020 at 15:58 | history | answered | Francesco Polizzi | CC BY-SA 4.0 |