Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Some Remarks on the Jacobian Conjecture and Dru{ż}kowski mappings (1302.5864v3)

Published 24 Feb 2013 in math.AG

Abstract: In this paper, we first show that the Jacobian Conjecture is true for non-homogeneous power linear mappings under some conditions. Secondly, we prove an equivalent statement about the Jacobian Conjecture in dimension $r\geq 1$ and give some partial results for $r=2$. Finally, for a homogeneous power linear Keller map $F=X+H$ of degree $d \ge 2$, we give the inverse polynomial map under the condition that $JH3=0$. We shall show that ${\operatorname{deg}}(F{-1})\leq dk$ if $k \le 2$ and $JH{k+1}=0$, but also give an example with $d = 2$ and $JH4=0$ such that ${\operatorname{deg}}(F{-1})> d3$.

Summary

We haven't generated a summary for this paper yet.