Geodesic
Three Remarks on the Inversion Problem for Polynomial Maps
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 94-97

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An example of covering a sphere by a projective plane arisen in relation to the so-called Jacobian problem is described. In the same relation, conformal types of complex curves are touched upon. The preservation of the type by multidimensional holomorphic maps is pointed out. 
@article{TM_2001_235_a5,
     author = {V. A. Zorich},
     title = {Three {Remarks} on the {Inversion} {Problem} for {Polynomial} {Maps}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {94--97},
     publisher = {mathdoc},
     volume = {235},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2001_235_a5/}
}
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V. A. Zorich. Three Remarks on the Inversion Problem for Polynomial Maps. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 94-97. http://geodesic.mathdoc.fr/item/TM_2001_235_a5/