The jacobian-conjecture tag has no wiki summary.

**2**

votes

**1**answer

71 views

### On transforming pair of bivariate polynomials to pair of univariate polynomials by applying polynomial map

We know that a polynomial map $f(x,y), g(x,y)$ is polynomial automorphism if there exists polynomials $p(x,y)$ and $q(x,y)$ such that $f(p,q)$=x and $g(p,q)=y$. Jacobian conjecture tries to ...

**1**

vote

**0**answers

80 views

### Jacobian Conjecture, Cubic-Keller maps

I have recently read an interesting article about the Jacobian Conjecture, in particular the reduction to the case $f(x) = x + A(x)^3$.
I was wondering about codimension one divisors on $Y = A^n$. ...

**1**

vote

**0**answers

205 views

### Weakened jacobian conjecture for entire functions

A rudin's theorem is the assertion that any polynomial injection between affine spaces of the same dimension has a polynomial inverse, and the inverse is also given by polynomials.
The jacobian ...

**6**

votes

**1**answer

653 views

### Could the Jacobian conjecture be undecidable?

Most of us know the Jacobian conjecture. Here's a version below for fixed positive integers $d$ and $n$:
$J(d,n)$: If $f: C^n \rightarrow C^n$ is a polynomial map of degree $d$, and if the Jacobian ...