Abstract
Grauert showed that it is possible to construct complete Kähler metrics on the complement of complex analytic sets in a domain of holomorphy. In this note, we study the holomorphic sectional curvatures of such metrics on the complement of a principal divisor in \(\mathbb {C}^n\), \(n \ge 1\). In addition, we also study how this metric and its holomorphic sectional curvature behave when the corresponding principal divisors vary continuously.
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