no. 2
SL 2 -equivariant polynomial automorphisms of the binary forms
Annales de l'Institut Fourier, Tome 47 (1997) no. 2, pp. 585-597.

Soit R n :=ℂ[x,y] n l’espace des formes binaires de degré n≥1. Nous montrons que chaque automorphisme polynomial de R n qui commute avec l’action linéaire de SL 2 (ℂ) et qui conserve la variété des formes avec racines deux à deux distinctes, est un multiple scalaire de l’identité sur R n .

We consider the space of binary forms of degree n≥1 denoted by R n :=ℂ[x,y] n . We will show that every polynomial automorphism of R n which commutes with the linear SL 2 (ℂ)-action and which maps the variety of forms with pairwise distinct zeroes into itself, is a multiple of the identity on R n .

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     author = {Kurth, Alexandre},
     title = {${\rm SL}_2$-equivariant polynomial automorphisms of the binary forms},
     journal = {Annales de l'Institut Fourier},
     pages = {585--597},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {47},
     number = {2},
     year = {1997},
     doi = {10.5802/aif.1574},
     zbl = {0974.14033},
     mrnumber = {98e:14049},
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     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1574/}
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Kurth, Alexandre. ${\rm SL}_2$-equivariant polynomial automorphisms of the binary forms. Annales de l'Institut Fourier, Tome 47 (1997) no. 2, pp. 585-597. doi : 10.5802/aif.1574. https://aif.centre-mersenne.org/articles/10.5802/aif.1574/

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