Essential dimensions of algebraic groups and a resolution theorem for G-varieties

Details Essential dimensions of algebraic groups and a resolution theorem for G-varieties Essential dimensions of algebraic groups and a resolution theorem for G-varieties

1999-03-28

arxiv.org/abs/math/9903162v3

Mathematics

Algebraic Geometry

This revision contains new lower bounds for essential dimensions of algebraic groups of types A_n and E_7. AMS LaTeX 1.1, 42 p

Scientific paper

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 U and a diagonalizable group A. 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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