Hessian幂零多项式的若干性质及公开问题
Some Properties of and Open Problems on Hessian Nilpotent Polynomials
摘要：
在最近的进展[BE 1]、[M]、[Z 1]和[Z 2]中，著名的Jacobian猜想（[BCW]、[E]）被归结为HN（Hessian nilpotent）多项式（其黑塞矩阵是幂零的多项式）及其（变形的）逆对的问题。本文证明了关于HN多项式及其（变形）反演对以及相应的对称多项式或形式映射的几个结果。我们还提出了一些有待进一步研究的问题。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
