Application of Multihomogeneous Covariants to the Essential Dimension of Finite Groups

Details Application of Multihomogeneous Covariants to the Essential Dimension of Finite Groups Application of Multihomogeneous Covariants to the Essential Dimension of Finite Groups

2008-11-24

arxiv.org/abs/0811.3852v1

Mathematics

Algebraic Geometry

34 pages, no figures

Scientific paper

We investigate essential dimension of finite groups over arbitrary fields and give a systematic treatment of multihomogenization, introduced by H.Kraft, G.Schwarz and the author. We generalize the central extension theorem of Buhler and Reichstein and use multihomogenization to substitute and generalize the stack-involved part of the theorem of Karpenko and Merkurjev about the essential dimension of p-groups. One part of this paper is devoted to the study of completely reducible faithful representations. Amongst results concerning faithful representations of minimal dimension there is a computation of the minimal number of irreducible components needed for a faithful representation.

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