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Branched coverings over \(\mathbb C^2\) and the Jacobian conjecture. (English. Russian original) Zbl 1068.14017
Math. Notes 76, No. 2, 161-169 (2004); translation from Mat. Zametki 76, No. 2, 172-182 (2004).
Summary: The class of branched coverings over \(\mathbb C^2\) traditionally called exotic arouses interest because of its connection with the Jacobian conjecture. In this paper, we construct a series of examples of such coverings; in particular, methods of construction of coverings with arbitrarily many sheets, as well as with unknotted branch curves, are described. In addition, some topological characteristics of these coverings are computed, which allows us to answer some questions about a possible counterexample to the Jacobian conjecture.
MSC:
14E20 Coverings in algebraic geometry
14R15 Jacobian problem
32Q99 Complex manifolds
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