23 citations · 43 across the 33 of their papers we have counts for
5 papers · 1 filter
The Groebner basis of a polynomial system
Christian Valqui, Marco Solorzano
We compute the Groebner basis of a system of polynomial equations related to the Jacobian conjecture using a recursive formula for the Catalan numbers.
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…
The starred Dixmier conjecture for
Christian Valqui, Vered Moskowicz
Let be the first Weyl algebra over a characteristic zero field and let be the exchange involution on given by a…
On the shape of possible counterexamples to the Jacobian Conjecture
Jorge A. Guccione, Juan J. Guccione, Christian Valqui
We improve the algebraic methods of Abhyankar for the Jacobian Conjecture in dimension two and describe the shape of possible counterexamples. We give an elementary proof of the re…