Computations of Keller maps over fields with \tfrac16

2016/09/30 by de Bondt, Michiel
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.09753

Abstract

We classify Keller maps x + H in dimension n over fields with \tfrac16, for which H is homogeneous, and (1) deg H = 3 and rk JH ≤ 2; (2) deg H = 3 and n ≤ 4; (3) deg H = 4 and n ≤ 3; (4) deg H = 4 = n and H₁, H₂, H₃, H₄ are linearly dependent over K. In our proof of these classifications, we formulate (and prove) several results which are more general than needed for these classifications. One of these results is the classification of all homogeneous polynomial maps H as in (1) over fields with \tfrac16.

Related

• Quadratic homogeneous polynomial maps H and Keller maps x+H with 3 ≤ \rm rk J H ≤ 4
• Quadratic homogeneous polynomial maps H and Keller maps x+H with rk JH=3
• Classification of cubic homogeneous polynomial maps with Jacobian matrices of rank two
• Irreducibility properties of Keller maps
• Generic degrees of real polynomial Keller maps with non-dense image