The classification of some polynomial maps with nilpotent Jacobians

Dan Yan; Michiel de Bondt

doi:10.1016/j.laa.2018.12.020

The classification of some polynomial maps with nilpotent Jacobians

Algebraic Geometry 2018-12-27 v3

Authors: Dan Yan , Michiel de Bondt

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Abstract

In the paper, we first classify all polynomial maps $H$ of the following form: $H=\big(H_1(x_1,x_2,\ldots,x_n),H_2(x_1,x_2),H_3(x_1,x_2),\ldots,H_n(x_1,x_2)\big)$ with $JH$ nilpotent. After that, we generalize the structure of $H$ to $H=\big(H_1(x_1,x_2,\ldots,x_n),H_2(x_1,x_2),H_3(x_1,x_2,H_1),\ldots,H_n(x_1,x_2,H_1)\big)$ .

Keywords

polynomial maps nilpotent Jacobian classification algebraic geometry polynomial mapping Jacobian matrix multivariable polynomials

Cite

@article{arxiv.1710.04210,
  title  = {The classification of some polynomial maps with nilpotent Jacobians},
  author = {Dan Yan and Michiel de Bondt},
  journal= {arXiv preprint arXiv:1710.04210},
  year   = {2018}
}

Comments

Major revision with some new results. arXiv admin note: text overlap with arXiv:1710.02802, arXiv:1710.02800

The classification of some polynomial maps with nilpotent Jacobians

Abstract

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