Essential Dimensions of Algebraic Groups and a Resolution Theorem for G-Varieties

Reichstein, Zinovy ; Youssin, Boris

Canadian journal of mathematics, Tome 52 (2000) no. 5, pp. 1018-1056

Résumé

Let $G$ be an algebraic group and let $X$ be a generically free $G$ -variety. We show that $X$ can be transformed, by a sequence of blowups with smooth $G$ -equivariant centers, into a $G$ -variety ${{X}^{'}}$ with the following property: the stabilizer of every point of ${{X}^{'}}$ is isomorphic to a semidirect product $U\rtimes A$ of a unipotent group $U$ and a diagonalizable group $A$ .As an application of this result, we prove new lower bounds on essential dimensions of some algebraic groups. We also show that certain polynomials in one variable cannot be simplified by a Tschirnhaus transformation.

Détail

DOI : 10.4153/CJM-2000-043-5

Mots-clés : 14L30, 14E15, 14E05, 12E05, 20G10

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