Geodesic
On four-sheeted polynomial mappings of $\mathbb C^2$. I. The case of an irreducible ramification curve
Matematičeskie zametki, Tome 64 (1998) no. 6, pp. 847-862.

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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. 
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A. V. Domrina; S. Yu. Orevkov. On four-sheeted polynomial mappings of $\mathbb C^2$. I. The case of an irreducible ramification curve. Matematičeskie zametki, Tome 64 (1998) no. 6, pp. 847-862. http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a5/

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