10 citations · 43 across the 42 of their papers we have counts for
4 papers · 1 filter
Increasing the degree of a possible counterexample to the Jacobian Conjecture from 100 to 108
Jorge Alberto Guccione, Juan José Guccione, Rodrigo Horruitiner +1
We list all the pairs with for any hypothetical counterexample to the plane Jacobian Conjecture and discard them all, except the pair…
The Jacobian Conjecture: Approximate roots and intersection numbers
Jorge Alberto Guccione, Juan José Guccione, Rodrigo Horruitiner +1
We translate the results of Yansong Xu into the language of~\cite{GGV1}, obtaining nearly the same formulas for the intersection number of Jacobian pairs, but with an inequality in…
A short and elementary proof of Jung's theorem
Christian Valqui, Jorge A. Guccione, Juan J. Guccione
We give a short and elementary proof of Jung's theorem, which states that for a field K of characteristic zero the automorphisms of K[x,y] are generated by elementary automorphisms…
A system of polynomial equations related to the Jacobian Conjecture
Jorge A. Guccione, Juan José Guccione, Christian Valqui
We prove that the Jacobian conjecture is false if and only if there exists a solution to a certain system of polynomial equations. We analyse the solution set of this system. In pa…