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SORIANO, H. L. Resolubilidade perto do conjunto característico para uma classe de campos vetoriais complexos. 2016. 73 f. Dissertação (Mestrado em Ciências – Matemática) – Instituto de Ciências Matemáticas e de Computação (ICMC/USP), São Carlos – SP. This dissertation deals with the solvability of complex vector field L = ∂/∂t+ (a(x) + ib(x))∂/∂x, b ̸≡ 0 defined on Ωε = (−ε, ε) × S1, ε > 0, near the characteristic set Σ = {0} × S1, where a and b are C∞ real-valued functions in (−ε, ε). The presented results show that solvability of L in a full neighborhood of Σ depends on the interplay between the order of vanishing of the functions a and b at x = 0. Key-words: Solvability, characteristic set, complex vector field.