Displaying similar documents to “Reductive group actions with one-dimensional quotient”

SL 2 -equivariant polynomial automorphisms of the binary forms

Alexandre Kurth (1997)

Annales de l'institut Fourier

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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 .

A nonlinearizable action of S 3 on ℂ 4

Gene Freudenburg, Lucy Moser-Jauslin (2002)

Annales de l’institut Fourier

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The main purpose of this article is to give an explicit algebraic action of the group S 3 of permutations of 3 elements on affine four-dimensional complex space which is not conjugate to a linear action.

On quasihomogeneous manifolds – via Brion-Luna-Vust theorem

Marco Andreatta, Jarosław A. Wiśniewski (2003)

Bollettino dell'Unione Matematica Italiana

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We consider a smooth projective variety X on which a simple algebraic group G acts with an open orbit. We discuss a theorem of Brion-Luna-Vust in order to relate the action of G with the induced action of G on the normal bundle of a closed orbit of the action. We get effective results in case G = S ⁢ L ⁢ n and dim ⁡ X ≤ 2 ⁢ n - 2 .