摘要翻译：
在最近的[BE1]、[M]、[Z1]和[Z2]中，著名的Jacobian猜想([BCW]、[E])被归结为关于HN（Hessian幂零）多项式（Hessian矩阵为幂零的多项式）及其变形反演对的问题。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。我们也提出了一些有待进一步研究的问题。
---
英文标题：
《Some Properties of and Open Problems on Hessian Nilpotent Polynomials》
---
作者：
Wenhua Zhao
---
最新提交年份：
2008
---
分类信息：

一级分类：Mathematics        数学
二级分类：Complex Variables        复变数
分类描述：Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数，自守群作用与形式，伪凸性，复几何，解析空间，解析束
--
一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--

---
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.
---
PDF链接：
https://arxiv.org/pdf/0704.1689