On the Equivalence of Elementary Chains of Monoidal Transformations of the Projective Plane

A. S. Bystrikov

M. V. Lomonosov Moscow State University

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.

UDC: 514.77

Received: 06.03.2002

DOI: 10.4213/mzm213

 English version: Mathematical Notes, 2003, 73:5, 611–617

Bibliographic databases:

• 
• 
• 
•