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

Published online by Cambridge University Press:  20 November 2018

Zinovy Reichstein  and
Boris Youssin
Zinovy Reichstein
Affiliation:
Department of Mathematics, Oregon State University, Corvallis, Oregon 97331-4506, U.S.A. email: zinovy@math.orst.edu
Boris Youssin
Affiliation:
Department of Mathematics and Computer Science, University of the Negev, Be’er Sheva’, Israel
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Abstract

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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.

Keywords

14L3014E1514E0512E0520G10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 52 , Issue 5 , 01 October 2000 , pp. 1018 - 1056
Copyright
Copyright © Canadian Mathematical Society 2000

References

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