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Mat. Zametki, 1998, Volume 64, Issue 6, Pages 847–862 (Mi mz1464)  

This article is cited in 10 scientific papers (total in 10 papers)

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

A. V. Domrinaa, S. Yu. Orevkovb

a 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.

DOI: https://doi.org/10.4213/mzm1464

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

Bibliographic databases:

UDC: 517.55
Received: 06.11.1997
Revised: 05.06.1998

Citation: A. V. Domrina, S. Yu. Orevkov, “On four-sheeted polynomial mappings of $\mathbb C^2$. I. The case of an irreducible ramification curve”, Mat. Zametki, 64:6 (1998), 847–862; Math. Notes, 64:6 (1998), 732–744

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. G. Vitushkin, “On the homology of a ramified covering over $\mathbb C^2$”, Math. Notes, 64:6 (1998), 726–731  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. V. Domrina, “Four-sheeted polynomial mappings in $\mathbb C^2$. The general case”, Math. Notes, 65:3 (1999), 386–389  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. A. V. Domrina, “On four-sheeted polynomial mappings of $\mathbb C^2$. II. The general case”, Izv. Math., 64:1 (2000), 1–33  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. S. Yu. Orevkov, “When a chain of blowups defines an automorphism of $\mathbb C^2$”, Math. Notes, 67:4 (2000), 541–543  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. S. Yu. Orevkov, “Counterexamples to the “Jacobian Conjecture at Infinity””, Proc. Steklov Inst. Math., 235 (2001), 173–201  mathnet  mathscinet  zmath
    6. G. V. Egorov, “Example of a Five-Sheeted Exotic Covering over $\mathbb C^2$”, Math. Notes, 71:4 (2002), 486–499  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. G. V. Egorov, “Branched Coverings over $\mathbb C^2$ and the Jacobian Conjecture”, Math. Notes, 76:2 (2004), 161–169  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. A. V. Domrina, “A Restriction on the Combinatorial Structure of Counterexamples to the Jacobian Conjecture at Infinity”, Proc. Steklov Inst. Math., 253 (2006), 51–56  mathnet  crossref  mathscinet  elib
    9. Zoladek H., “An application of Newton-Puiseux charts to the Jacobian problem”, Topology, 47:6 (2008), 431–469  crossref  mathscinet  zmath  isi  scopus  scopus
    10. Borisov A., “On Two Invariants of Divisorial Valuations At Infinity”, J. Algebr. Comb., 39:3 (2014), 691–710  crossref  mathscinet  zmath  isi  scopus  scopus
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