Abstract
Affine algebraic surfaces of Markov type of the form
are studied. Their automorphism groups are found.
Similar content being viewed by others
References
H. Flenner, S. Kaliman, and M. Zaidenberg, “Birational transformations of weighted graphs,” in Affine Algebraic Geometry (Osaka Univ. Press, Osaka, 2007), pp. 107–147; “Corrigendum,” in Affine Algebraic Geometry, 54 (Amer. Math. Soc. , Providence, RI, 2011), pp. 35–38.
A. Markoff, “Sur les formes quadratiques binaires indéfinies,” Math. Ann. 15, 381–406 (1879).
A. A. Markoff, “Sur les formes quadratiques binaires indéfinies II,” Math. Ann. 17, 379–399 (1880).
M. Aigner, Markov’s Theorem and 100 Years of the Uniqueness Conjecture (Springer, Cham, 2013).
U. Rehmann and E. Vinberg, “On a phenomenon discovered by Heinz Helling,” Transform. Groups 22, 259–265 (2017).
I. Arzhantsev and S. Gaifullin, “The automorphism group of a rigid affine variety,” Math. Nachr. 290 (5-6), 662–671 (2017).
A. Bjorner, F. Cohen, C. De Concini, C. Procesi, and M. Salvetti, Configuration Spaces. Geometry, Combinatorics and Topology (Edizioni della Normale, Pisa, 2012).
S. Kaliman, F. Kutzschebauch, and M. Leuenberger, “Complete algebraic vector fields on affine surfaces,” Internat. J. Math. 31 (3) (2020), Paper no. 2050018.
M. H. Èl’-Huti, “Cubic surfaces of Markov type,” Math. USSR-Sb. 22 (3), 333–348 (1974).
É. Ghys and V. Sergiescu, “Sur un groupe remarquable de difféomorphismes du cercle,” Comment. Math. Helv. 62 (2), 185–239 (1987).
A. Fossas, “\(\mathrm{PSL}(2,\mathbb Z)\) as a non-distorted Subgroup of Thompson’s group \(T\),” Indiana Univ. Math. J. 60 (6), 1905–1925 (2011).
J. Diller and J.-L. Lin, “Rational surface maps with invariant meromorphic two-forms,” Math. Ann. 364 (1-2), 313–352 (2016).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Matematicheskie Zametki, 2021, Vol. 110, pp. 744–750 https://doi.org/10.4213/mzm13263.
Rights and permissions
About this article
Cite this article
Perepechko, A.Y. Automorphisms of Surfaces of Markov Type. Math Notes 110, 732–737 (2021). https://doi.org/10.1134/S0001434621110109
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434621110109