Pluripolar hulls and convergence sets

Abstract

The pluripolar hull of a pluripolar set E in Pn is the intersection of all complete pluripolar sets in Pn that contain E. We prove that the pluripolar hull of each compact pluripolar set in Pn is F . The convergence set of a divergent formal power series f(z0; : : : ; zn) is the set of all \directions" 2 Pn along which f is convergent. We prove that the union of the pluripolar hulls of a countable collection of compact pluripolar sets in Pn is the convergence set of some divergent series f, which is more general than the result of Ma and Neelon (J. Complex Analysis and its Synergies 1:4 2015). The convergence sets on ?? := f[1 : z : (z)] : z 2 Cg C2 P2, where is a transcendental entire holomorphic function, are also studied and we obtain that a subset on ?? is a convergence set in P2 if and only if it is a countable union of compact projectively convex sets and that the union of a countable collection of convergence sets on ?? is a convergence set.