Geodesic
On the Equivalence of Elementary Chains of Monoidal Transformations of the Projective Plane
Matematičeskie zametki, Tome 73 (2003) no. 5, pp. 649-656 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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