Geodesic
On the Equivalence of Elementary Chains of Monoidal Transformations of the Projective Plane
Matematičeskie zametki, Tome 73 (2003) no. 5, pp. 649-656 
A. S. Bystrikov. On the Equivalence of Elementary Chains of Monoidal Transformations of the Projective Plane. Matematičeskie zametki, Tome 73 (2003) no. 5, pp. 649-656. http://geodesic.mathdoc.fr/item/MZM_2003_73_5_a1/
@article{MZM_2003_73_5_a1,
     author = {A. S. Bystrikov},
     title = {On the {Equivalence} of {Elementary} {Chains} of {Monoidal} {Transformations} of the {Projective} {Plane}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {649--656},
     year = {2003},
     volume = {73},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_5_a1/}
}
TY  - JOUR
AU  - A. S. Bystrikov
TI  - On the Equivalence of Elementary Chains of Monoidal Transformations of the Projective Plane
JO  - Matematičeskie zametki
PY  - 2003
SP  - 649
EP  - 656
VL  - 73
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_2003_73_5_a1/
LA  - ru
ID  - MZM_2003_73_5_a1
ER  - 
%0 Journal Article
%A A. S. Bystrikov
%T On the Equivalence of Elementary Chains of Monoidal Transformations of the Projective Plane
%J Matematičeskie zametki
%D 2003
%P 649-656
%V 73
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_2003_73_5_a1/
%G ru
%F MZM_2003_73_5_a1

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

We introduce the notion of curve associated with a chain of blow-ups of a complex surface. On the basis of this notion, we classify elementary chains (of length up to seven) of blow-ups of the projective plane. We prove (under an additional condition) that the ramification curve of the inverse of a polynomial mapping cannot be isolated in 4 or 5 blow-ups.

[1] Vitushkin A. G., “Vychislenie yakobiana ratsionalnogo preobrazovaniya $\mathbb C^2$ i nekotorye prilozheniya”, Matem. zametki, 66:2 (1999), 308–312 | MR | Zbl

[2] Vitushkin A. G., “Nekotorye primery v svyazi s problemoi obrascheniya polinomialnykh otobrazhenii $\mathbb C^n$”, Izv. AN SSSR. Ser. matem., 35 (1971), 269–279 | MR | Zbl

[3] Orevkov S. Yu., “Diagrammy Rudolfa i analiticheskaya realizatsiya nakrytiya Vitushkina”, Matem. zametki, 60:2 (1996), 206–224 | MR | Zbl

[4] Vitushkin A. G., Kriterii predstavimosti tsepochki $\sigma$-protsessov kompozitsiei treugolnykh tsepochek, 65:5 (1999) | MR | Zbl