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\(\text{SL}_2\)-equivariant polynomial automorphisms of the binary forms. (English) Zbl 0974.14033

Summary: We consider the space of binary forms of degree \(n\geq 1\) denoted by \(R_n :={\mathbb C}[x,y]_n\). We will show that every polynomial automorphism of \(R_n\) which commutes with the linear \(\text{SL}_2 ({\mathbb C})\)-action and which maps the variety of forms with pairwise distinct zeroes into itself, is a multiple of the identity on \(R_n\).

MSC:

14L30 Group actions on varieties or schemes (quotients)
14E07 Birational automorphisms, Cremona group and generalizations
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