Some Properties of and Open Problems on Hessian Nilpotent Polynomials

Details Some Properties of and Open Problems on Hessian Nilpotent Polynomials Some Properties of and Open Problems on Hessian Nilpotent Polynomials

2007-04-13

arxiv.org/abs/0704.1689v2

Ann. Polon. Math. 93 (2008), no. 2, 135--162.

Mathematics

Complex Variables

Latex, 33 pages. Some misprints have been corrected; English and also terminology for some newly defined notion have been impr

Scientific paper

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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