Some properties of and open problems on Hessian nilpotent polynomials

Wenhua Zhao. "Some properties of and open problems on Hessian nilpotent polynomials." Annales Polonici Mathematici 93.2 (2008): 135-162. <http://eudml.org/doc/280849>.

@article{WenhuaZhao2008,
abstract = {In the recent work [BE1], [Me], [Burgers] and [HNP], the well-known Jacobian conjecture ([BCW], [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.},
author = {Wenhua Zhao},
journal = {Annales Polonici Mathematici},
keywords = {Hessian nilpotent polynomial; jacobian conjecture; inversion pair; harmonic polynomial},
language = {eng},
number = {2},
pages = {135-162},
title = {Some properties of and open problems on Hessian nilpotent polynomials},
url = {http://eudml.org/doc/280849},
volume = {93},
year = {2008},
}

TY - JOUR
AU - Wenhua Zhao
TI - Some properties of and open problems on Hessian nilpotent polynomials
JO - Annales Polonici Mathematici
PY - 2008
VL - 93
IS - 2
SP - 135
EP - 162
AB - In the recent work [BE1], [Me], [Burgers] and [HNP], the well-known Jacobian conjecture ([BCW], [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.
LA - eng
KW - Hessian nilpotent polynomial; jacobian conjecture; inversion pair; harmonic polynomial
UR - http://eudml.org/doc/280849
ER -