Affine Space Bundles and Linearization

Hanspeter Kraft

Math Institute Basel

Brandeis University

Thursday, September 23, 2010

Talk at 4:30 p.m. in 317 Goldsmith Hall

Tea at 4:00 p.m. in 300 Goldsmith Hall

Abstract: The linearization problem asks if an action of a reductive algebraic group on complex affine $n$-space $A^n$ is equivalent to a linear representation. For $A^2$ this is indeed the case, due to the structure of the automorphism group of $A^2$ as an amalgamated product. However, it does not hold in dimension $>2$. The first counterexamples were given by G. W. Schwarz in 1989; they initiated an interesting development. A related object in this setting are affine space bundles, i.e. morphisms with all fibers isomorphic to affine $n$-space. Here the fundamental question is if such a morphism is locally trivial in some reasonable sense. We will describe some highlights, some open problems and some recent developments.

Home Web page: Alexandru I. Suciu Posted: September 14, 2010
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