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1. CJM 2000 (vol 52 pp. 1018)

Reichstein, Zinovy; Youssin, Boris
 Essential Dimensions of Algebraic Groups and a Resolution Theorem for \$G\$-Varieties 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 \sdp 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. Categories:14L30, 14E15, 14E05, 12E05, 20G10

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