SL 2 -equivariant polynomial automorphisms of the binary forms
Kurth, Alexandre
Annales de l'Institut Fourier, Tome 47 (1997), p. 585-597 / Harvested from Numdam
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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 .

@article{AIF_1997__47_2_585_0,
     author = {Kurth, Alexandre},
     title = {${\rm SL}\_2$-equivariant polynomial automorphisms of the binary forms},
     journal = {Annales de l'Institut Fourier},
     volume = {47},
     year = {1997},
     pages = {585-597},
     doi = {10.5802/aif.1574},
     mrnumber = {98e:14049},
     zbl = {0974.14033},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1997__47_2_585_0}
}

Kurth, Alexandre. ${\rm SL}_2$-equivariant polynomial automorphisms of the binary forms. Annales de l'Institut Fourier, Tome 47 (1997) pp. 585-597. doi : 10.5802/aif.1574. http://gdmltest.u-ga.fr/item/AIF_1997__47_2_585_0/

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