In this paper we give an update survey of the most important results concerning the Jacobian conjecture: several equivalent descriptions are given and various related conjectures are discussed. Atâ€¦ (More)

The Image Conjecture was formulated by the third author, who showed that it implied his Vanishing Conjecture, which is equivalent to the famous Jacobian Conjecture. We prove various cases of theâ€¦ (More)

In this paper, we present an unexpected link between the Factorial Conjecture ([8]) and Furterâ€™s Rigidity Conjecture ([13]). The Factorial Conjecture in dimension m asserts that if a polynomial f inâ€¦ (More)

It is shown that the Jacobian Conjecture holds for all polynomial maps F : k â†’ k of the form F = x + H , such that JH is nilpotent and symmetric, when n â‰¤ 4. If H is also homogeneous a similar resultâ€¦ (More)

In this paper it is established that all two-dimensional polynomial automorphisms over a regular ring R are stably tame. This results from the main theorem of this paper, which asserts that anâ€¦ (More)

Let k be a field of characteristic zero and F : k â†’ k a polynomial map of the form F = x + H, where H is homogeneous of degree d â‰¥ 2. We show that the Jacobian Conjecture is true for such mappings.â€¦ (More)

We give a polynomial counterexample to a discrete version of the Markus-Yamabe Conjecture and a conjecture of Deng, Meisters and Zampieri, asserting that if F : C â†’ C is a polynomial map with det(JFâ€¦ (More)