Year: 2020
Type: preprint
Abstract: For given natural numbers $d_1,d_2$ let $Ω_2(d_1,d_2)$ be the set off all polynomial mappings $F=(f,g):\mathbb{C}^2\to\mathbb{C}^2$ such that deg $f\le d_1$, deg $g\le d_2$. We say that the mapping $F$ is topologically stable in $Ω_2(d_1,d_2)$ if for every small deformation $F_t\in Ω_2(d_1,d_2)$ the mapping $F_t$ is topologically equivalent to the mapping $F$. The aim of this paper is to characterize the topologically stable mappings in $Ω_2(d_1,d_2)$. In particular we show how to effectively determine a member of $Ω_2(d_1,d_2)$ with generic topology.
Source: arXiv (Cornell University)
Authors: Farnik, Michał, Jelonek, Zbigniew
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3034456272