Polynomial maps with nilpotent Jacobians in dimension three I

2017/10/08 by Dan Yan, Yan, Dan
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1710.02800

openalex publication_date 2017/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we first prove that u,v,h are linearly dependent over \bf K if JH is nilpotent and H has the form: H=(u(x,y,z),v(u,h),h(x,y)) with H(0)=0 or H=(u(x,y),v(u,h),h(x,y,z)) with H(0)=0. Then we classify polynomial maps of the form H=(u(x,y),v(x,y,z), h(x,y)) in the case that JH is nilpotent and (°_yu,°_yh)≤ 2.

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