On locally trivial G a -actions

Autor: J. K. Deveney, D. R. Finston
Rok vydání: 1997
Předmět:
Zdroj: Transformation Groups. 2:137-145
ISSN: 1531-586X
1083-4362
DOI: 10.1007/bf01235937
Popis: If the additive group of complex numbers acts algebraically on a normal affine variety, then the associated ring of invariants need not be finitely generated, but is an ideal transform of some normal affine algebra (Theorem 1). We investigate such normal affine algebras in the case of a locally trivial action on a factorial variety. If the variety is a complex affine space and the ring of invariants is isomorphic to a polynomial ring, then the action is conjugate to a translation (Theorem 3). Equivalently, ifC n , is the total space for a principalG a -bundle over some open subset ofCn−1 then the bundle is trivial. On the other hand, there is a locally trivialG a -action on a normal affine variety with nonfinitely generated ring of invariants (Theorem 2).
Databáze: OpenAIRE
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