Geodesic
The Markov numbers and exceptional bundles on $\mathbf P^2$
Izvestiya. Mathematics, Tome 32 (1989) no. 1, pp. 99-112 
A. N. Rudakov. The Markov numbers and exceptional bundles on $\mathbf P^2$. Izvestiya. Mathematics, Tome 32 (1989) no. 1, pp. 99-112. http://geodesic.mathdoc.fr/item/IM2_1989_32_1_a5/
@article{IM2_1989_32_1_a5,
     author = {A. N. Rudakov},
     title = {The {Markov} numbers and exceptional bundles on~$\mathbf P^2$},
     journal = {Izvestiya. Mathematics},
     pages = {99--112},
     year = {1989},
     volume = {32},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1989_32_1_a5/}
}
TY  - JOUR
AU  - A. N. Rudakov
TI  - The Markov numbers and exceptional bundles on $\mathbf P^2$
JO  - Izvestiya. Mathematics
PY  - 1989
SP  - 99
EP  - 112
VL  - 32
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IM2_1989_32_1_a5/
LA  - en
ID  - IM2_1989_32_1_a5
ER  - 
%0 Journal Article
%A A. N. Rudakov
%T The Markov numbers and exceptional bundles on $\mathbf P^2$
%J Izvestiya. Mathematics
%D 1989
%P 99-112
%V 32
%N 1
%U http://geodesic.mathdoc.fr/item/IM2_1989_32_1_a5/
%G en
%F IM2_1989_32_1_a5

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

The author establishes a one-to-one correspondence between the natural solutions of the Markov equation $x^2+y^2+z^2=3xyz$ and the exceptional bundles on the projective plane whose slopes belong to the interval $\biggl[0,\dfrac12\biggr]$. He also studies the properties of exceptional bundles and exact sequences connecting them. Bibliography: 8 titles.

[1] Gorshkov D. S., “Geometriya Lobachevskogo v svyazi s nekotorymi voprosami arifmetiki”, Zap. nauch. semin. LOMI, 67, 1977, 39–85 | Zbl

[2] Kassels D. V. S., Vvedenie v teoriyu diofantovykh priblizhenii, IL, M., 1961

[3] Malyshev A. V., “Spektry Markova i Lagranzha (obzor literatury)”, Zap. nauch. semin. LOMI, 67, 1977, 5–37

[4] Markov A. A., O binarnykh kvadratichnykh formakh polozhitelnogo opredelitelya, SPb., 1880, 44 pp.

[5] Cohn H., “Markoff forms and primitive words”, Math. Ann., 196:1 (1972), 8–22 | DOI | MR | Zbl

[6] Dfezet J. M., Le Potter J., “Fibrés stables et fibrés exceptionnels sur $\mathbf{P}^2$”, Ann. Ser. ENS, 18:2 (1985), 193–244 | MR

[7] Rosen D., Patterson G. S., “Some numerical evidence concerning the uniqueness of Markov numbers”, Math. Comput., 25:116 (1971), 919–921 | DOI | MR | Zbl

[8] Rosenberger G., “The uniqueness of the Markov numbers”, Math. Comput., 30:134 (1976), 361–365 | DOI | MR | Zbl