# On Proper Polynomial Maps of $mathbb{C}^2.$ - Mathematics > Complex Variables

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Abstract: Two proper polynomial maps $f 1, f 2 \colon \mathbb{C}^2 \longrightarrow\mathbb{C}^2$ are said to be \emph{equivalent} if there exist $\Phi 1, \Phi 2\in \textrm{Aut}\mathbb{C}^2$ such that $f 2=\Phi 2 \circ f 1 \circ \Phi 1$.We investigate proper polynomial maps of arbitrary topological degree $d \geq2$ up to equivalence. Under the further assumption that the maps are Galoiscoverings we also provide the complete description of equivalence classes. Thiswidely extends previous results obtained by Lamy in the case $d=2$.

Author: Cinzia Bisi, Francesco Polizzi

Source: https://arxiv.org/