Some properties of and open problems on Hessian nilpotent polynomials
Volume 93 / 2008
Annales Polonici Mathematici 93 (2008), 135-162
MSC: 14R15, 32H02, 32A50.
DOI: 10.4064/ap93-2-3
Abstract
In the recent work \cite{BE1}, \cite{Me}, \cite{Burgers} and \cite{HNP}, the well-known Jacobian conjecture (\cite{BCW}, \cite{E}) has been reduced to a problem on HN (Hessian nilpotent) polynomials (the polynomials whose Hessian matrix is nilpotent) and their (deformed) inversion pairs. In this paper, we prove several results on HN polynomials, their (deformed) inversion pairs as well as on the associated symmetric polynomial or formal maps. We also propose some open problems for further study.
