Non-negative divisors and the Grauert metric

Sahil Gehlawat; Kaushal Verma

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arXiv · 2103.16458

Non-negative divisors and the Grauert metric

Sahil Gehlawat·Kaushal Verma

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Abstract

Grauert showed that it is possible to construct complete K\"{a}hler 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 behaves when the corresponding principal divisors vary continuously.

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Sahil Gehlawat, Kaushal Verma. 2021-03-30. Non-negative divisors and the Grauert metric. https://arxiv.org/abs/2103.16458

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