1 research outputs found
Some Properties of and Open Problems on Hessian Nilpotent Polynomials
In the recent progress [BE1], [M], [Z1] and [Z2], the well-known Jacobian
conjecture ([BCW], [E]) has been reduced to a problem on HN (Hessian nilpotent)
polynomials (the polynomials whose Hessian matrix are nilpotent) and their
(deformed) inversion pairs. In this paper, we prove several results on HN
polynomials, their (deformed) inversion pairs as well as the associated
symmetric polynomial or formal maps. We also propose some open problems for
further study of these objects.Comment: Latex, 33 pages. Some misprints have been corrected; English and also
terminology for some newly defined notion have been improved. To appear in
Annales Polonici Mathematic