Classification of cubic homogeneous polynomial maps with Jacobian matrices of rank two

2018/03/15 by de Bondt, Michiel, Sun, Xiaosong
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.05551

Abstract

Let K be any field with \textupcharK≠ 2,3. We classify all cubic homogeneous polynomial maps H over K with \textuprk JH≤ 2. In particular, we show that, for such an H, if F=x+H is a Keller map then F is invertible, and furthermore F is tame if the dimension n≠ 4.

Related

• Quadratic homogeneous polynomial maps H and Keller maps x+H with rk JH=3
• Quadratic homogeneous polynomial maps H and Keller maps x+H with 3 ≤ \rm rk J H ≤ 4
• Irreducibility properties of Keller maps
• Computations of Keller maps over fields with \tfrac16
• Some Results On The Jacobian Conjecture And Polynomial Automorphisms