Plane Jacobian Conjecture for Rational Polynomials
نویسندگان
چکیده
We verify the plane Jacobian conjecture for the rational polynomials: A polynomial map F = (P, Q) : C −→ C, P, Q ∈ C[x, y], is invertible if PxQy − PyQx ≡ const. 6= 0 and, in addition, P is a rational polynomial, i.e. the generic fiber of P is the 2-dimensional topological sphere with a finite number of punctures.
منابع مشابه
Plane Jacobian problem for rational polynomials
This paper is to present a geometrical proof of the plane Jacobian conjecture for rational polynomials by an approach of Newton-Puiseux data and geometry of rational surfaces. The obtained result shows that a polynomial map F = (P, Q) : C −→ C with PxQy − PyQx ≡ const. 6= 0 has a polynomial inverse if the component P is a rational polynomial, i.e. if the generic fiber of P is the 2-dimensional ...
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The said paper [Su2] entitled " Proof Of Two Dimensional Jacobian Conjecture " is false. Comments The Jacobian Conjecture is a well-known hard problem. Recently there are many attempts to solve it. This paper is one of the false attempts. Minor mistakes We have read Su's latest version (Dec 30, 2005) of his papers. There are numerous typos (say, some d ′ s, and all d ′ i s really should be d 2 ...
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