Geodesic
On the positivity of direct image bundles
Izvestiya. Mathematics , Tome 87 (2023) no. 5, pp. 987-1010

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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.
Keywords: $L^2$-methods, plurisubharmonic functions, positive hermitian holomorphic vector bundles, minimal principles, relative Bergman kernel.
Mots-clés : direct images 
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Zhi Li; Xiangyu Zhou. On the positivity of direct image bundles. Izvestiya. Mathematics , Tome 87 (2023) no. 5, pp. 987-1010. http://geodesic.mathdoc.fr/item/IM2_2023_87_5_a8/