On the positivity of direct image bundles

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Abstract

In the present paper, we obtain an equivalent relation between the log-plurisubharmonicity of the relative Bergman kernel, the Griffiths and Nakano positivity for the direct image with the natural $L^2$ metric, by finding a converse of Berndtsson’s Theorem on the direct image. A converse of Berndtsson’s generalization of Kiselman minimal principle is also obtained.

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About the authors

Zhi Li

School of Science, Beijing University of Posts and Telecommunications

Xiangyu Zhou

Academy of Mathematics and Systems Science, Chinese Academy of Sciences; Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences

Email: xyzhou@math.ac.cn
PhD

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