On the Jacobian conjecture
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Abstract:
We show that the Jacobian conjecture can be reduced to a weaker conjecture in which all fibers of coordinate functions are irreducible.References
- Shreeram Abhyankar, Über die endliche Erzeugung der Fundamentalgruppe einer komplex-algebraischen Mannigfaltigkeit, Math. Ann. 139 (1960), 265–274 (1960) (German). MR 114815, DOI 10.1007/BF01352262
- Hyman Bass, Edwin H. Connell, and David Wright, The Jacobian conjecture: reduction of degree and formal expansion of the inverse, Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 2, 287–330. MR 663785, DOI 10.1090/S0273-0979-1982-15032-7
- Edward Formanek, Two notes on the Jacobian conjecture, Arch. Math. (Basel) 49 (1987), no. 4, 286–291. MR 913158, DOI 10.1007/BF01210711
- D. B. Fuks and V. A. Rokhlin, Beginner’s course in topology, Universitext, Springer-Verlag, Berlin, 1984. Geometric chapters; Translated from the Russian by A. Iacob; Springer Series in Soviet Mathematics. MR 759162, DOI 10.1007/978-3-642-61755-3
- Ott-Heinrich Keller, Ganze Cremona-Transformationen, Monatsh. Math. Phys. 47 (1939), no. 1, 299–306 (German). MR 1550818, DOI 10.1007/BF01695502
- David Mumford, Algebraic geometry. I, Grundlehren der Mathematischen Wissenschaften, No. 221, Springer-Verlag, Berlin-New York, 1976. Complex projective varieties. MR 0453732
- James Morrow and Kunihiko Kodaira, Complex manifolds, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1971. MR 0302937
- Walter Neumann and Lee Rudolph, Unfoldings in knot theory, Math. Ann. 278 (1987), no. 1-4, 409–439. MR 909235, DOI 10.1007/BF01458078
- Michael Razar, Polynomial maps with constant Jacobian, Israel J. Math. 32 (1979), no. 2-3, 97–106. MR 531253, DOI 10.1007/BF02764906
- Yosef Stein, On linear differential operators related to the Jacobian conjecture, J. Pure Appl. Algebra 57 (1989), no. 2, 175–186. MR 985658, DOI 10.1016/0022-4049(89)90114-X
- Yosef Stein, The total reducibility order of a polynomial in two variables, Israel J. Math. 68 (1989), no. 1, 109–122. MR 1035885, DOI 10.1007/BF02764973
- Yosef Stein, On linear differential operators related to the Jacobian conjecture, J. Pure Appl. Algebra 57 (1989), no. 2, 175–186. MR 985658, DOI 10.1016/0022-4049(89)90114-X
- Stuart Sui Sheng Wang, A generalization of a lemma of Abhyankar and Moh, J. Pure Appl. Algebra 40 (1986), no. 3, 297–299. MR 836655, DOI 10.1016/0022-4049(86)90048-4
- Oscar Zariski, On the Problem of Existence of Algebraic Functions of Two Variables Possessing a Given Branch Curve, Amer. J. Math. 51 (1929), no. 2, 305–328. MR 1506719, DOI 10.2307/2370712
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 45-51
- MSC: Primary 14E07; Secondary 13B10, 14E20
- DOI: https://doi.org/10.1090/S0002-9939-1993-1106179-7
- MathSciNet review: 1106179