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CLOSED SUBGROUPS OF THE POLYNOMIAL AUTOMORPHISM GROUP CONTAINING THE AFFINE SUBGROUP

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Abstract

We prove that, in characteristic zero, closed subgroups of the polynomial automorphisms group containing the affine group contain the whole tame group.

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References

  1. J. Blanc, A. Calabri, On degenerations of plane Cremona transformations, Math. Zeitschrift 282 (2014), no. 1, 223–245.

    MathSciNet  MATH  Google Scholar 

  2. Y. Bodnarchuk, Some extreme properties of the affine group as an automorphisms group of the affine space, Contribution to General Algebra 13 (2001), 15–29.

    MathSciNet  MATH  Google Scholar 

  3. Y. Bodnarchuk, Generating properties of triangular and bitriangular birational automorphisms of affine space, Dopov. NAN Ukrainy (2002), no. 11, 7–22.

  4. E. Edo, P.-M. Poloni, On the closure of the tame automorphism group of affine three-space, Inter. Math. Research Notices (2015), doi: 10.1093/imrn/rnu237.

  5. A. van den Essen, Polynomial Automorphisms and the Jacobian Conjecture, Progress in Mathematics, Vol. 190, Birkhäuser Verlag, Basel, 2000.

  6. J.-P. Furter, Polynomial composition rigidity and plane polynomial automorphisms, J. London Math. Soc. 91 (2015), no. 1, 180–202.

    Article  MathSciNet  MATH  Google Scholar 

  7. J.-P. Furter, H. Kraft, On the geometry of the automorphism group of affine n-space, in preparation (2015).

  8. H. W. E. Jung, Über ganze birationale Transformationen der Ebene, J. Reine Angew. Math. 184 (1942), 161–174.

    MathSciNet  MATH  Google Scholar 

  9. W. van der Kulk, On polynomial rings in two variables, Nieuw. Arch. Wisk. (3) 1 (1953), 33–41.

  10. S. Kuroda, Degeneration of tame automorphisms of a polynomial ring, Comm. In Algebra 44 (2016), no. 3, 1196–1199.

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Nagata, On Automorphism Group of k[x; y], Lectures in Mathematics, Department of Mathematics, Kyoto University, Vol. 5, Kinokuniya, Tokyo, 1972.

  12. И. P. Шaфapeвич, O нeкoтopыx бecкoнeчнoмepныx гpуппax. II, Извecтия AH CCCP. Cep. мaтeм. 45 (1981), вьш. 1, 214–226. Engl. transl.: I. R. Shafarevich, On some infinite-dimensional groups II, Math. USSR-Izv. 18 (1982), no. 1, 185–194.

  13. I. Shestakov, U. Umirbaev, The tame and the wild automorphisms of polynomial rings in three variables, J. Amer. Math. Soc. 17 (2004), 197–227.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. ERIM, University of New Caledonia, BP R4-98851, Nouméa CEDEX, New Caledonia, France

    ERIC EDO

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  1. ERIC EDO
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EDO, E. CLOSED SUBGROUPS OF THE POLYNOMIAL AUTOMORPHISM GROUP CONTAINING THE AFFINE SUBGROUP. Transformation Groups 23, 71–74 (2018). https://doi.org/10.1007/s00031-016-9412-7

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  • DOI: https://doi.org/10.1007/s00031-016-9412-7

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