Timeline for Special elements of the Cremona group
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 27, 2019 at 16:56 | vote | accept | user237522 | ||
| Nov 27, 2019 at 13:59 | answer | added | Jérémy Blanc | timeline score: 2 | |
| Nov 25, 2019 at 3:40 | comment | added | user237522 | @YCor, thank you for the clarification. | |
| Nov 24, 2019 at 19:04 | comment | added | YCor | What I meant was the following natural problem: characterize, if possible in an "algorithmic" way, those pairs $(u(x,y),v(x,y)$ that are induced by some automorphism. Typically computing a Jacobian is what I mean by "algorithmic". | |
| Nov 24, 2019 at 14:29 | comment | added | user237522 | @YCor, please, could you elaborate on one of your previous comments: "But in Cremona 'describe the group' can have a totally different meaning. E.g., it can consist in describing the set of pairs of rational functions that indeed define a element of the Cremona group..." | |
| Nov 24, 2019 at 14:26 | comment | added | user237522 | @YCor, you are right... but at least it is a finite product of such, though writing a general pair (as a pair of elements of $\mathbb{C}[x,y]$) is impossible... Any other suggestions? (Or a similar result for a pair of polynomials not being a Jacobian pair?). | |
| Nov 24, 2019 at 13:58 | comment | added | YCor | But an automorphism of $C[x,y]$ is not always affine or triangular... | |
| Nov 24, 2019 at 13:56 | history | edited | user237522 | CC BY-SA 4.0 |
added 63 characters in body
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| Nov 24, 2019 at 13:51 | comment | added | user237522 | @YCor, thanks, good question.. Perhaps something similar to 'a general form' of a $\mathbb{C}$-algebra automorphism of $\mathbb{C}[x,y]$ (affine or triangular). But other types of answers are welcome too. (Actually, I wished to restrict to the case where $\operatorname{Jac}(u,v) \in \mathbb{C}[x,y]-\mathbb{C}$ to exclude, by Keller's theorem, automorphisms of $\mathbb{C}[x,y]$; I will add this). | |
| Nov 24, 2019 at 12:59 | comment | added | YCor | What do you mean by "a general form"? | |
| Nov 24, 2019 at 12:59 | history | edited | YCor | CC BY-SA 4.0 |
made more precise
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| Nov 24, 2019 at 12:34 | history | asked | user237522 | CC BY-SA 4.0 |