A note on the Jacobian Conjecture
Copyright policy )A note on the Jacobian Conjecture
In this note, we show that, if the Druzkowski mappings $F(X)=X+(AX)^{*3}$, i.e. $F(X)=(x_1+(a_{11}x_1+...+a_{1n}x_n)^3,...,x_n+(a_{n1}x_1+...+a_{nn}x_n)^3)$, satisfies $TrJ((AX)^{*3})=0$, then $rank(A)\leq 1/2(n+δ)$ where $δ$ is the number of diagonal elements of A which are equal to zero. Furthermore, we show the Jacobian Conjecture is true for the Druzkowski mappings in dimension $\leq 9$ in the case $\prod_{i=1}^{n}a_{ii}\neq0$.
5 pages
- University of Chinese Academy of Sciences China (People's Republic of)
- GRADUATE UNIVERSITY OF CHINESE ACADEMY OF SCIENCES China (People's Republic of)
- Chinese Academy of Sciences China (People's Republic of)
Jacobian Conjecture, Numerical Analysis, Polynomial mapping, Algebra and Number Theory, Jacobian problem, Druzkowski mapping, polynomial mapping, Mathematics - Algebraic Geometry, Jacobian conjecture, FOS: Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Rational and birational maps, Algebraic Geometry (math.AG)
Jacobian Conjecture, Numerical Analysis, Polynomial mapping, Algebra and Number Theory, Jacobian problem, Druzkowski mapping, polynomial mapping, Mathematics - Algebraic Geometry, Jacobian conjecture, FOS: Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Rational and birational maps, Algebraic Geometry (math.AG)
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