Geodesic
Automorphisms of Surfaces of Markov Type
Matematičeskie zametki, Tome 110 (2021) no. 5, pp. 744-750.

Voir la notice de l'article provenant de la source Math-Net.Ru

Affine algebraic surfaces of Markov type of the form $$ x^2+y^2+z^2-xyz=c $$ are studied. Their automorphism groups are found.
Mots-clés : affine surface, automorphism group, birational transformations
Keywords: Thompson group, Markov numbers, boundary divisor. 
@article{MZM_2021_110_5_a8,
     author = {A. Yu. Perepechko},
     title = {Automorphisms of {Surfaces} of {Markov} {Type}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {744--750},
     publisher = {mathdoc},
     volume = {110},
     number = {5},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_5_a8/}
}
TY  - JOUR
AU  - A. Yu. Perepechko
TI  - Automorphisms of Surfaces of Markov Type
JO  - Matematičeskie zametki
PY  - 2021
SP  - 744
EP  - 750
VL  - 110
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_110_5_a8/
LA  - ru
ID  - MZM_2021_110_5_a8
ER  - 
%0 Journal Article
%A A. Yu. Perepechko
%T Automorphisms of Surfaces of Markov Type
%J Matematičeskie zametki
%D 2021
%P 744-750
%V 110
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2021_110_5_a8/
%G ru
%F MZM_2021_110_5_a8
A. Yu. Perepechko. Automorphisms of Surfaces of Markov Type. Matematičeskie zametki, Tome 110 (2021) no. 5, pp. 744-750. http://geodesic.mathdoc.fr/item/MZM_2021_110_5_a8/

[1] H. Flenner, S. Kaliman, M. Zaidenberg, “Birational transformations of weighted graphs”, Affine Algebraic Geometry, Osaka Univ. Press, Osaka, 2007, 107–147 ; “Corrigendum”, Affine Algebraic Geometry, 54, CRM Proc. Lecture Notes, Providence, RI, 2011, 35–38 | MR | Zbl | MR | Zbl

[2] A. Markoff, “Sur les formes quadratiques binaires indéfinies”, Math. Ann., 15 (1879), 381–406 | DOI

[3] A. A. Markoff, “Sur les formes quadratiques binaires indéfinies II”, Math. Ann., 17 (1880), 379–399 | DOI | MR

[4] M. Aigner, Markov's Theorem and 100 Years of the Uniqueness Conjecture, Springer, Cham, 2013 | DOI | MR

[5] U. Rehmann, E. Vinberg, “On a phenomenon discovered by Heinz Helling”, Transform. Groups, 22 (2017), 259–265 | DOI | MR | Zbl

[6] I. Arzhantsev, S. Gaifullin, “The automorphism group of a rigid affine variety”, Math. Nachr., 290:5-6 (2017), 662–671 | DOI | MR | Zbl

[7] A. Bjorner, F. Cohen, C. De Concini, C. Procesi, M. Salvetti, Configuration Spaces. Geometry, Combinatorics and Topology, Edizioni della Normale, Pisa, 2012 | MR | Zbl

[8] S. Kaliman, F. Kutzschebauch, M. Leuenberger, “Complete algebraic vector fields on affine surfaces”, Internat. J. Math., 31:3 (2020), 2050018 | DOI | MR | Zbl

[9] M. Kh. El-Khuti, “Kubicheskie poverkhnosti markovskogo tipa”, Matem. sb., 93 (135):3 (1974), 331–346 | MR | Zbl

[10] É. Ghys, V. Sergiescu, “Sur un groupe remarquable de difféomorphismes du cercle”, Comment. Math. Helv., 62:2 (1987), 185–239 | DOI | MR | Zbl

[11] A. Fossas, “$\mathrm{PSL}(2,\mathbb Z)$ as a non-distorted Subgroup of Thompson's group $T$”, Indiana Univ. Math. J., 60:6 (2011), 1905–1925 | MR

[12] J. Diller, J.-L. Lin, “Rational surface maps with invariant meromorphic two-forms”, Math. Ann., 364:1-2 (2016), 313–352 | DOI | MR | Zbl