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Non-negative divisors and the Grauert metric

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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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Acknowledgements

The authors would like to thank the referee for carefully reading the article and giving suggestions to improve the previous version of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Science, Bangalore, 560 012, India

    Sahil Gehlawat & Kaushal Verma

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  1. Sahil Gehlawat
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  2. Kaushal Verma
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Correspondence to Sahil Gehlawat.

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SG is supported by CSIR-SPM Ph.D. fellowship.

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Gehlawat, S., Verma, K. Non-negative divisors and the Grauert metric. Arch. Math. 119, 311–323 (2022). https://doi.org/10.1007/s00013-022-01762-w

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  • DOI: https://doi.org/10.1007/s00013-022-01762-w

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