Lê Dũng Tráng; Weber, Claude A geometrical approach to the Jacobian conjecture for \(n=2\). (English) Zbl 1128.14301 Kodai Math. J. 17, No. 3, 374-381 (1994). Summary: Let us recall the Jacobian conjecture: “Jacobian Conjecture. Let \(F: \mathbb C^n \to \mathbb C^n\) be a polynomial map. Suppose that, for every point \(x \in \mathbb C^n\), the derivative \(F' (x)\) is invertible. Then the map \(F\) is invertible.”In this lecture we describe a geometrical approach to this conjecture when \(n=2\). Cited in 1 ReviewCited in 17 Documents MSC: 14E07 Birational automorphisms, Cremona group and generalizations 13F20 Polynomial rings and ideals; rings of integer-valued polynomials 14E05 Rational and birational maps PDFBibTeX XMLCite \textit{Lê Dũng Tráng} and \textit{C. Weber}, Kodai Math. J. 17, No. 3, 374--381 (1994; Zbl 1128.14301) Full Text: DOI References: [1] E. Artal, Une demonstration Geometrique du theoreme d’AbhyanJcar-Moh, [2] S. Abhyankar, T. T. Moh, Embeddings of the line in the plane, Jr. Angw. Reine Math. 27 (1975), 148-166. · Zbl 0332.14004 [3] H. Bass, E. H. Connell, D. Wright, The Jacobian Conjecture: reduction of degree and forma expansion of the inverse, Bull. Amer. Math. Soc. 7, (1982), 287-330. · Zbl 0539.13012 · doi:10.1090/S0273-0979-1982-15032-7 [4] S. A. Broughton, Milnor numbers and the topology of polynomial hypersurfaces, Inv. Math. 9 (1988), 217-241. · Zbl 0658.32005 · doi:10.1007/BF01404452 [5] Ha Huy Vui: Le Dung Trang, Sur la topologie des polynmes complexes, Acta Math. Vietn. (1984), 21-32. · Zbl 0597.32005 [6] Le Dung Trang, F. Michel, C. Weber, Sur le comportement des polaires associees au germes de courbes planes, Comp. Math. 72 (1989), 87-113. · Zbl 0705.32021 [7] T. T. Moh, On analytic irreducibility at oo of a pencil of curves, Proc. Amer. Math. Soc. 4 (1974), 22-24. · Zbl 0309.14011 · doi:10.2307/2039219 [8] D. Mumford, Algebraic Geometry I, Complex Algebraic Varieties, Grundlehren der math. Wis senschaften 221, Springer Verlag (1976). · Zbl 0356.14002 [9] S. Yu. Orevkov, On three-sheeted polynomial mappings of C2, Math. USSR Izvestiya, 2 (1987), 587-596. · Zbl 0633.13005 · doi:10.1070/IM1987v029n03ABEH000984 [10] A. G. Vitushkin, Certain examples in connections with problems about polynomial transfer mations of Cn, Math. USSR Izvestiya, 5 (1971), 278-288. · Zbl 0248.32020 · doi:10.1070/IM1971v005n02ABEH001046 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.