#### Z. Reichstein, B. Youssin, *
Essential Dimensions of Algebraic Groups and a Resolution Theorem
for G-varieties *, with an appendix by J. Kollar and E. Szabo,
Canadian J. Math., 52, no. 5 (2000), 1018 - 1056.

** Abstract: **
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
of a unipotent group and a diagonalizable group.
As an application of this and related results, 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.

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