A. Essen

activity

20062019

most citedOn the equivalence of the Jacobian, Dixmier and Poisson Conjectures in any characteristic

6 citations · 14 across the 6 of their papers we have counts for

collaborators

6 papers

math.AC2019★ 4 cited

An introduction to Mathieu subspaces

Arno van den Essen

This is the note for the four lectures given by the author in the ``International Short-School/Conference on Affine Algebraic Geometry and the Jacobian Conjecture" at Chern Institu…

math.AC2019

Mathieu-Zhao spaces of polynomial rings

Arno van den Essen, Loes van Hove

We describe all Mathieu-Zhao spaces of $k [x_{1}, \dots, x_{n}]$ ( $k$ is an algebraically closed field of characteristic zero) which contains an ideal of finite codimension. Furthermore…

math.AC2008

A note on k[z]-automorphisms in two variables

Eric Edo, Arno van den Essen, Stefan Maubach

We prove that for a polynomial $f \in k [x, y, z]$ equivalent are: (1) $f$ is a $k [z]$ -coordinate of $k [z] [x, y]$ , and (2) $k [x, y, z] / (f) ≅ k^{[2]}$ and $f (x, y, a)$ is a coordinate in $…

math.AG2008

A commuting derivations theorem on UFDs

Harm Derksen, Arno van den Essen, Stefan Maubach

Let $A$ be the polynomial ring over $k$ (a field of characteristic zero) in $n + 1$ variables. The commuting derivations conjecture states that $n$ commuting locally nilpotent deriva…

math.AG2007★ 4 cited

Two Results on Homogeneous Hessian Nilpotent Polynomials

Arno van den Essen, Wenhua Zhao

Let $z = (z_{1}, ..., z_{n})$ and $Δ = \sum_{i = 1}^{n} \frac{\partial ^{2}}{\partial z _{i}^{2}}$ the Laplace operator. A formal power series $P (z)$ is said to be {\it Hessian Nilpotent}(HN) if its…

math.AG2006★ 6 cited

On the equivalence of the Jacobian, Dixmier and Poisson Conjectures in any characteristic

Kossivi Adjamagbo, Arno van den Essen

Thanks to recent results on ring homomorphisms of Azumaya algebras and to the following ones about endomorphisms of canonical Poisson algebras and Dirac quantum algebras, and about…