Abstract The convergence set of a divergent formal power series $$f(x_{0},dots ,x_{n})$$ f ( x 0 , ? , x n ) is the set of all “directions” $$xi in $$ ξ ∈ $$mathbb {P}^{n}$$ P n along which f is absolutely convergent. We prove that every countable union of closed complete pluripolar sets in $$mathbb {P}^{n}$$ P n is the convergence set of some divergent series f . The (affine) convergence sets of formal power series with polynomial coefficients are also studied. The higher-dimensional analogs of the results of Sathaye (J Reine Angew Math 283:86–98, 1976), Lelong (Proc Am Math Soc 2:11–19, 1951), Levenberg and Molzon (Math Z 197:411–420, 1988), and of Ribón (Ann Scuola Norm Sup Pisa Cl Sci (5) 3:657–680 2004) are obtained.
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机译：摘要发散形式幂级数$$ f（x_ {0}， dots，x_ {n}）$$ f（x 0，？，xn）的收敛集是所有“方向” $$ xi的集合 in $$ξ∈$$ mathbb {P} ^ {n} $$ P n，f绝对收敛。我们证明，$$ mathbb {P} ^ {n} $$ P n中的闭合完整多极集的每个可数并集都是某个散列级数f的收敛集。还研究了具有多项式系数的形式幂级数的（仿射）收敛集。 Sathaye（J Reine Angew Math 283：86–98，1976），Lelong（Proc Am Math Soc 2：11–19，1951），Levenberg和Molzon（Math Z 197：411-420）的结果的高维类似物，1988年）和Ribón（Ann Scuola Norm Sup Pisa Cl Sci（5）3：657–680 2004）。
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