Timeline for A variation on Abhyankar–Moh–Suzuki theorem
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Dec 29, 2021 at 6:24 | answer | added | pinaki | timeline score: 1 | |
| Dec 29, 2021 at 1:10 | vote | accept | user237522 | ||
| Dec 28, 2021 at 21:39 | answer | added | Jérémy Blanc | timeline score: 3 | |
| Dec 23, 2021 at 12:56 | comment | added | user237522 | If $\deg(f)=\deg(g)=n$ and $\deg(h)=n-1$ (so $\deg(f_1)=\deg(g_1)=1$), then I think it is not difficult to show that $t \mapsto (f(t),g(t))$ is injective, so with new condition (4) we obtain that $\mathbb{C}[f,g]=\mathbb{C}[t]$. But for $\deg(h) \geq 2$ and $\deg(f_1)=\deg(g_1) \geq 2$, I do not know how to show that $t \mapsto (f(t),g(t))$ is injective. | |
| Dec 22, 2021 at 23:56 | history | edited | user237522 | CC BY-SA 4.0 |
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| Dec 22, 2021 at 23:39 | comment | added | user237522 | Therefore, and in view of idea (i), we will add the condition that $f',g'$ are not simultaneously zero. Then, the above counterexample is not a counterexample anymore, since $f'=15t^{14}+2t$, $g'=15t^{14}$ have a common zero at $0$. | |
| Dec 22, 2021 at 23:21 | comment | added | user237522 | $f=t^{15}+t^2$, $g=t^{15}$ is a counterexample.... | |
| Dec 22, 2021 at 23:20 | history | edited | user237522 | CC BY-SA 4.0 |
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| Dec 22, 2021 at 23:00 | history | edited | user237522 | CC BY-SA 4.0 |
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| Dec 22, 2021 at 22:21 | history | edited | user237522 | CC BY-SA 4.0 |
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| Dec 22, 2021 at 19:31 | history | edited | user237522 | CC BY-SA 4.0 |
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| Dec 22, 2021 at 19:14 | history | edited | user237522 | CC BY-SA 4.0 |
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| Dec 22, 2021 at 19:05 | history | edited | LSpice | CC BY-SA 4.0 |
Edited link to Q295158 per https://mathoverflow.net/questions/412323/a-variation-on-abhyankar-moh-suzuki-theorem#comment1056641_412323
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| Dec 22, 2021 at 19:04 | comment | added | user237522 | @LSpice, no, it was not intensional. Thank you for letting me know. | |
| Dec 22, 2021 at 18:59 | comment | added | LSpice | Your second question link (mathoverflow.net/questions/295158/…) goes to an answer. Was that intentional? | |
| Dec 22, 2021 at 18:59 | history | edited | user237522 | CC BY-SA 4.0 |
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| Dec 22, 2021 at 18:59 | history | edited | LSpice | CC BY-SA 4.0 |
`|` -> `\mid`; inline question links
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| Dec 22, 2021 at 18:55 | history | asked | user237522 | CC BY-SA 4.0 |