A POLAR, THE CLASS AND PLANE JACOBIAN CONJECTURE

Title & Authors
A POLAR, THE CLASS AND PLANE JACOBIAN CONJECTURE
Joe, Do-Sang;

Abstract
Let P be a Jacobian polynomial such as deg P = $\small{deg_y}$ P. Suppose the Jacobian polynomial P satisfies the intersection condition satisfying $\small{dim_C}$ C[x, y]/> = deg P - 1, we can prove that the Keller map which has P as one of coordinate polynomial always has its inverse.
Keywords
polar;class of plane curve;plane Jacobian conjecture;
Language
English
Cited by
References
1.
S. S. Abhyankar, Algebraic Geometry for Scientists and Engineers, Mathematical Surveys and Monographs, 35. American Mathematical Society, Providence, RI, 1990.

2.
S. S. Abhyankar and T. Moh, Embeddings of the line in the plane, J. Reine Angew. Math. 276 (1975), 148–166.

3.
E. Brieskorn and H. Knorrer, Plane Algebraic Curves, Birkhauser Verlag, Basel, 1986.

4.
N. V. Chau, Plane Jacobian polynomial for rational polynomials, preprint, arXiv: 0804.3172v2

5.
D. Cox, J. Little, and D. O'Shea, Using Algebraic Geometry, Second edition. Graduate Texts in Mathematics, 185. Springer, New York, 2005.

6.
A. van den Essen, Polynomial Automorphisms and the Jacobian Conjecture, Birkhauser Verlag, Basel, 2000.

7.
A. van den Essen and J. Yu, The D-resultant, singularities and the degree of unfaithfulness, Proc. Amer. Math. Soc. 125 (1997), no. 3, 689–695.

8.
I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky, Discriminants, Resultants and Multidimensional Determinants, Birkhauser Boston, Inc., Boston, MA, 1994.

9.
R. C. Heitmann, On the Jacobian conjecture, J. Pure Appl. Algebra 64 (1990), no. 1, 35–72.

10.
D. Joe and H. Park, Emdeddings of line in the plane and Abhynkar-Moh epimorphism theorem, Bull. Korean. Math. Soc. 46 (2009), no. 1, 171–182.

11.
T. Moh, On the Jacobian conjecture and the configurations of roots, J. Reine Angew. Math. 340 (1983), 140–212.

12.
M. Razar, Polynomial maps with constant Jacobian, Israel J. Math. 32 (1979), no. 2-3, 97–106.

13.
L. D. Trang, Simple rational polynomials and the Jacobian conjecture, Publ. Res. Inst. Math. Sci. 44 (2008), no. 2, 641–659.