Abstract
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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Bystrikov, A.S. On the Equivalence of Elementary Chains of Monoidal Transformations of the Projective Plane. Mathematical Notes 73, 611–617 (2003). https://doi.org/10.1023/A:1024000402593
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DOI: https://doi.org/10.1023/A:1024000402593