Weak positivity theorem and Frobenius stable canonical rings of geometric generic fibers

Ejiri, Sho

doi:10.1090/jag/698

Author: Sho Ejiri
Journal: J. Algebraic Geom. 26 (2017), 691-734
DOI: https://doi.org/10.1090/jag/698
Published electronically: June 2, 2017
MathSciNet review: 3683424
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Abstract | References | Additional Information

Abstract: In this paper, we prove the weak positivity theorem in positive characteristic when the canonical ring of the geometric generic fiber $F$ is finitely generated and the Frobenius stable canonical ring of $F$ is large enough. As its application, we show the subadditivity of Kodaira dimensions in some new cases.

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Additional Information

Sho Ejiri
Affiliation: Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
Email: ejiri@ms.u-tokyo.ac.jp

Received by editor(s): August 10, 2015
Received by editor(s) in revised form: August 31, 2016
Published electronically: June 2, 2017
Additional Notes: The author wishes to express his gratitude to his supervisor, Professor Shunsuke Takagi, for suggesting the problems in this paper, for answering many questions, and for much helpful advice. The author is also grateful to Professors Yifei Chen, Yoshinori Gongyo and Zsolt Patakfalvi for valuable comments and discussions. He would like to thank Professor Akiyoshi Sannai and Doctors Takeru Fukuoka, Kenta Sato, and Fumiaki Suzuki for useful comments. He also wishes to thank the referee for the careful reading and valuable suggestions. The author was supported by JSPS KAKENHI grant No. 15J09117 and the Program for Leading Graduate Schools, MEXT, Japan
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