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Fundamental, Picard, and Class Groups of Rings of Invariants

Published online by Cambridge University Press:  20 November 2018

Andy R. Magid
Andy R. Magid*
Affiliation:
The University of Oklahoma, Norman, Oklahoma
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Let G be a n affine algebraic group over the algebraically closed field k, and let V be an affine, normal algebraic variety over k on which G acts. Suppose that the ring of invariants k [F]G is finitely generated over k, and let W be the affine variety with k[W] = k[V]G. The purpose of this paper is to show that the induced homomorphism from the étale fundamental group of V to that of W is surjective, and to examine the consequences of this observation in terms of the relations between the Picard and divisor class groups of k[V] and k[W],

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 3 , 01 June 1976 , pp. 659 - 664
Copyright
Copyright © Canadian Mathematical Society 1976

References

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