Geodesic
On the Equivalence of Elementary Chains of Monoidal Transformations of the Projective Plane
Matematičeskie zametki, Tome 73 (2003) no. 5, pp. 649-656

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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. 
@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},
     publisher = {mathdoc},
     volume = {73},
     number = {5},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_5_a1/}
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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/