Abstract
We establish a relative Bertini type theorem for multiplier ideal sheaves. Then we prove a relative version of the Kollár-Nadel type vanishing theorem as an application.
Acknowledgments
The author was partially supported by JSPS KAKENHI Grant Numbers JP16H03925, JP16H06337, JP19H01787, JP20H00111, JP21H00974. He would like to thank Shin-ichi Matsumura and Haidong Liu very much for some useful comments. He also would like to thank Professor Sébastien Boucksom for comments on [9] and Professor Mattias Jonsson for comments at the conference: Stability, Boundedness and Fano Varieties. Finally, he thanks the referee and Mingchen Xia very much.
Citation
Osamu Fujino. "Relative Bertini type theorem for multiplier ideal sheaves." Osaka J. Math. 60 (1) 207 - 226, January 2023.
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