Pluripotential theory on analytic sets and applications to algebraicity. (Q1396094)

The aim of the paper is to give a quantitative version of Sadullaev's criterion of algebraicity for complex analytic sets [\textit{A. Sadullaev}, Math. USSR, Izv. 20, 493--502 (1983); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 46, 524--534 (1982; Zbl 0511.32010)] in terms of their local behaviour in the spirit of the author's earlier paper [Acta Math. 184, 113--143 (2000; Zbl 1016.32015)]. Moreover, it is shown that the criterion of algebraicity can be extended to real analytic sets.