This article is cited in 13 papers

On four-sheeted polynomial mappings of $\mathbb C^2$. I. The case of an irreducible ramification curve

A. V. Domrina^a, S. Yu. Orevkov<sup>b

a</sup> M. V. Lomonosov Moscow State University
^b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The paper is devoted to the Jacobian Conjecture: a polynomial mapping $f\colon\mathbb C^2\to\mathbb C^2$ with a constant nonzero Jacobian is polynomially invertible. The main result of the paper is as follows. There is no four-sheeted polynomial mapping whose Jacobian is a nonzero constant such that after the resolution of the indeterminacy points at infinity there is only one added curve whose image is not a point and does not belong to infinity.

UDC: 517.55

Received: 06.11.1997
Revised: 05.06.1998

DOI: 10.4213/mzm1464

 English version: Mathematical Notes, 1998, 64:6, 732–744

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