Abstract
We study the reduction problem for a holomorphic singular vector field with nilpotent linear part at the origin, P = (y + a(X)) ∂x + (z + b(X)) ∂y + c(X)∂z, where X = (x, y, z) ∈ C3. By introducing a notion of quasi-valuation, which was given in the previous paper [M-S] with A. Shirai, we characterize a class which can be reduced into simpler ones by formal change of coordinates which admit various variations in Theorems A and B.
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