Reduced Forms of a Singular Vector Field in $\mathbf{C}^3$ with Nilpotent Linear Partm

MR3364476 Masatake MIYAKE Masatake MIYAKE Reduced Forms of a Singular Vector Field in $\mathbf{C}^3$ with Nilpotent Linear Partm Funkcialaj Ekvacioj. Serio Internacia 58 2015 253--275 http://fe.math.kobe-u.ac.jp/FE/FullPapers/58-2/58_253.pdf http://www.ams.org/mathscinet-getitem?mr=MR3364476 We study the reduction problem for a holomorphic singular vector field with nilpotent linear part at the origin, $P=(y+a(X))\partial_x+(z+b(X))\partial_y+c(X)\partial_z$, where $X=(x,y,z)\in\mathbf{C}^3$. 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. Nilpotent vector field, Normal forms, Formal reduction. Primary 32M25, 32S65, Secondary 35A20, 35F05. 58-253 2015 Reduced Forms of a Singular Vector Field in $\mathbf{C}^3$ with Nilpotent Linear Part Masatake MIYAKE Masatake MIYAKE

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