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math.CV2025
Proof of the metric Arnold's corank problem
Aexandre Fernandes, Zbigniew Jelonek, José Edson Sampaio
In this article, we approach the Arnold corank problem, posed by Arnold in 1975, which asks whether the corank of holomorphic functions is an ambient topological invariant. Here, w…
math.CV2024
On the topological invariance of the algebraic multiplicity of holomorphic foliations
Leonardo M. Câmara, Fernando Reis, José Edson Sampaio
In this paper, we address one of the most basic and fundamental problems in the theory of foliations and ODEs, the topological invariance of the algebraic multiplicity of a holomor…