Abstract
In this note we show that if the automorphism group of a normal affine surface S is isomorphic to the automorphism group of a Danielewski surface, then S is isomorphic to the normalization of a Danielewski surface.
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W. Danielewski, On a cancellation problem and automorphism groups of affine algebraic varieties, preprint, Warsaw (1989).
J.-P. Furter, H. Kraft, On the geometry of the automorphism groups of affine varieties, arXiv:1809.04175 (2018).
H. Flenner, M. Zaidenberg, Normal affine surfaces with ℂ*-actions, Osaka J. Math. 40 (2003), no. 4, 981–1009.
H. Flenner, M. Zaidenberg, Locally nilpotent derivations on affine surfaces with a ℂ*-action, Osaka J. Math. 42 (2005), no. 4, 931–974.
R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York, 1977.
F. Kutzschebauch, M. Leuenberger, The Lie algebra generated by locally nilpotent derivations on a Danielewski surface, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 15 (2016), 183–207.
M. Leuenberger, A. Regeta, Vector fields and automorphism groups of Danie-lewski surfaces, to appear in Int. Math. Res. Not., arXiv:1710.06045 (2017).
A. Liendo, A. Regeta, C. Urech, Characterization of affine surfaces with a torus action by their automorphism groups, arXiv:1805.03991v3 (2020).
L. Makar-Limanov, On groups of automorphisms of a class of surfaces, Israel J. Math. 69 (1990), no. 2, 250–256.
L. Makar-Limanov, On the group of automorphisms of a surface xny = P(z), Israel J. Math. 121 (2001), no. 1, 113–123.
P. Orlik, P.Wagreich, Algebraic surfaces with k*-action, Acta Math. 138 (1977), no. 1-2, 43–81.
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ALVARO LIENDO is partially supported by Fondecyt projects 1160864 and 1200502.
CHRISTIAN URECH is supported by the SNF, project number P2BSP2 175008.
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LIENDO, A., REGETA, A. & URECH, C. ON THE CHARACTERIZATION OF DANIELEWSKI SURFACES BY THEIR AUTOMORPHISM GROUPS. Transformation Groups 27, 181–187 (2022). https://doi.org/10.1007/s00031-020-09606-z
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DOI: https://doi.org/10.1007/s00031-020-09606-z