RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy MIAN: Year: Volume: Issue: Page: Find

 Tr. Mat. Inst. Steklova, 2001, Volume 235, Pages 181–210 (Mi tm244)

Counterexamples to the “Jacobian Conjecture at Infinity”

S. Yu. Orevkov

Abstract: Earlier, the author constructed an example of an open complex surface $U$, a smooth compact rational curve $L\subset U$ with the self-intersection index $+1$, and a holomorphic immersion $f:U\setminus L\to\mathbb C^2$ that is meromorphic on $U$ but is not an embedding (if $U\subset \mathbb C\mathrm P^2$, then such an immersion can be extended to a counterexample to the Jacobian conjecture). In this paper, an analogous example is constructed with the property that $f|_{\partial U}$ is an immersion of a 3-sphere in $\mathbb C^2$ which is regularly homotopic to an embedding. The map $f$ cannot be extended to a counterexample to the Jacobian conjecture, which is proved by the analysis of the coefficients of polynomials.

Full text: PDF file (464 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 235, 173–201

Bibliographic databases:
UDC: 512.77

Citation: S. Yu. Orevkov, “Counterexamples to the “Jacobian Conjecture at Infinity””, Analytic and geometric issues of complex analysis, Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin, Tr. Mat. Inst. Steklova, 235, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 181–210; Proc. Steklov Inst. Math., 235 (2001), 173–201

Citation in format AMSBIB
\Bibitem{Ore01} \by S.~Yu.~Orevkov \paper Counterexamples to the Jacobian Conjecture at Infinity'' \inbook Analytic and geometric issues of complex analysis \bookinfo Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin \serial Tr. Mat. Inst. Steklova \yr 2001 \vol 235 \pages 181--210 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm244} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1886583} \zmath{https://zbmath.org/?q=an:1009.14012} \transl \jour Proc. Steklov Inst. Math. \yr 2001 \vol 235 \pages 173--201 

• http://mi.mathnet.ru/eng/tm244
• http://mi.mathnet.ru/eng/tm/v235/p181

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. 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
2. Zoladek H., “An application of Newton–Puiseux charts to the Jacobian problem”, Topology, 47:6 (2008), 431–469
•  Number of views: This page: 256 Full text: 80 References: 30