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Some Properties of and Open Problems on Hessian Nilpotent Polynomials

Authors
  • Zhao, Wenhua
Type
Published Article
Publication Date
Feb 24, 2008
Submission Date
Apr 13, 2007
Identifiers
arXiv ID: 0704.1689
Source
arXiv
License
Unknown
External links

Abstract

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.

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