Non-negative divisors and the Grauert metric (Q2166355)

In [Math. Ann. 131, 38--75 (1956; Zbl 0073.30203)], \textit{H. Grauert} proved that every domain of holomorphy admits a real analytic, complete Kähler metric. The converse is not true, in fact it is possible to construct complete Kähler metrics on the complement of complex analytic sets in a domain of holomorphy. The aim of the paper is to study the holomorphic sectional curvature of such metrics on the complement of a principal divisor in \(\mathbb{C}^n\) when \(n \geq 1\). Eventually, the authors study how this metric behaves when the corresponding principal divisors vary in a continuous way.