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. 
@article{MZM_1998_64_6_a5,
     author = {A. V. Domrina and S. Yu. Orevkov},
     title = {On four-sheeted polynomial mappings of $\mathbb C^2$. {I.} {The} case of an irreducible ramification curve},
     journal = {Matemati\v{c}eskie zametki},
     pages = {847--862},
     publisher = {mathdoc},
     volume = {64},
     number = {6},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a5/}
}
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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/