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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Nonsingular affine $ k\sp *$-surfaces


Author: Jean Rynes
Journal: Trans. Amer. Math. Soc. 332 (1992), 889-921
MSC: Primary 14L30; Secondary 14J50
MathSciNet review: 1062868
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Abstract: Nonsingular affine $ {k^{\ast} }$-surfaces are classified as certain invariant open subsets of projective $ {k^{\ast}}$-surfaces. A graph is defined which is an equivariant isomorphism invariant of an affine $ {k^{\ast}}$-surface. Over the complex numbers, it is proved that the only acyclic affine surface which admits an effective action of the group $ {{\mathbf{C}}^{\ast} }$ is $ {{\mathbf{C}}^2}$ which admits only linear actions of $ {{\mathbf{C}}^{\ast}}$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1062868-8
PII: S 0002-9947(1992)1062868-8
Article copyright: © Copyright 1992 American Mathematical Society