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Ga-Action of the Affine Plane

Published online by Cambridge University Press:  22 January 2016

Masayoshi Miyanishi
Masayoshi Miyanishi*
Affiliation:
Kyoto University
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Recently, R. Rentschler [4] proved that if k is a field of characteristic 0, any action of the additive group Ga on the affine plane is equivalent to an action of the form t(x, y) = (x, y + tf(x), where t∈Ga(k), (x, y)∈k2 and f∈k[X].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 41 , February 1971 , pp. 97 - 100
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

[1] Grothendieck, A. et Dieudouné, J., Eléments de Géométrie Algébrique (referred to as EGA), Chapitres III et IV, Publ. Math. Inst. Hautes Etudes Sci., No. 11 and 24.Google Scholar
[2] Miyanishi, M., A remark on an iterative infinite higher derivation, J. Math. Kyoto Univ., 8 (1968), 411–415.Google Scholar
[3] Nagata, M., Note on orbit spaces, Osaka Math. J., 14 (1962), 21–31.Google Scholar
[4] Rentschler, R., Opérations du groupe additif sur le plan affine, C.R. Acad. Soc. Paris, 267 (1968), 384–387.Google Scholar
[5] Springer, T.A., On a lemma of Rosenlicht, Indagationes Mathematicae, 30 (1968), 378–383.Google Scholar