Non-negative divisors and the Grauert metric

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 C n , n ≥ 1.In addition, we also study how this metric and its holomorphic sectional curvature behave when the corresponding principal divisors vary continuously.