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Sufficiently Homogeneous Closed Embeddings of 𝔸n-1 into 𝔸n are Linear

Published online by Cambridge University Press:  20 November 2018

Peter Russell
Peter Russell*
Affiliation:
Department of Mathematics & Statistics, McGill University, Montreal, PQ and Centre Interuniversitaire en Calcul Mathématique Algébrique (CICMA)
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Abstract

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We show that over a field k of characteristic zero an affine (n — 1)- space embedded as a closed subvariety in affine n-space and homogeneous for a codimension two linear torus action on is defined by the vanishing of a variable.

Keywords

14E2514E09
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 6 , 01 December 1996 , pp. 1286 - 1295
Copyright
Copyright © Canadian Mathematical Society 1996

References

[A] Abhyankar, S. S., Expansion Techniques in Algebraic Geometry, Tata Institute of Fundamental Research, Lecture Notes on Mathematics and Physics, Bombay (1977).Google Scholar
[AM] Abhyankar, S. S. and Moh, T.-T., Embeddings of the line in the plane, J. Reine Angew. Math. 276(1975), 148–166.Google Scholar
[B-B] Bialynicki-Birula, A., Remarks on the action of an algebraic torus on kn, I and II, Bull. Acad. Pol. Sci. 14(1966), 177–181 and 15(1967), 123-125.Google Scholar
[BH] Bass, H. and Haboush, W., Linearizing certain reductive group actions, Trans. Am. Math. Soc. (2)292 (1985), 463–481.Google Scholar
[KbR] Kambayashi, T. and Russell, P., On linearizing algebraic torus actions, J. Pure Appl. Algebra 23(1982), 243–250.Google Scholar
[KR1] Koras, M. and Russell, P., On linearizing “good” C*-actions on C3, Can. Math. Soc. Conf. Proc. 10 (1989), 92–102.Google Scholar
[KR2] Koras, M. and Russell, P., Codimension 2 torus actions on affine n-space, Canad. Math. Soc. Conf. Proc. 10(1989), 103—110.Google Scholar
[KR3] Koras, M. and Russell, P., Contractible threefolds and C*-actions on C3 , manuscript, CICMA preprint series.Google Scholar
[KR4] Koras, M. and Russell, P., On C3/C*; the smooth locus is not of hyperbolic type, in preparation.Google Scholar
[PTD] Petrie, T. and Tom Dieck, T., The Abhyankar-Moh problem in dimension 3, Springer Lecture Notes in Mathematics 1375(1989), 48–59.Google Scholar
[RS] Russell, P. and Sathaye, A., Onfinding and cancelling variables in k[X, Y,Z], J. Alg. (1)57(1979), 151–166.Google Scholar
[S] Suzuki, M., Propriétés topologiques des polynomes de deux variables complexes et automorphismes algébriques de Vespace C2, J. Math. Soc. Japan 26(1974), 241–257.Google Scholar