A note on families of K-semistable log-Fano pairs

In proceeding: Cheltsov, I., Chen, X., Katzarkov, L., Park, J. (eds) Birational Geometry, K\"ahler--Einstein Metrics and Degenerations, 2019, Springer Proceedings in Mathematics \& Statistics, vol 409, page 195--203 In this short note, we give an alternative proof of the semipositivity of t...

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Bibliographic Details
Main Authors Codogni, Giulio, Patakfalvi, Zsolt
Format Journal Article
LanguageEnglish
Published 16.07.2021
Subjects
Mathematics - Algebraic Geometry
Mathematics - Differential Geometry
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Summary:In proceeding: Cheltsov, I., Chen, X., Katzarkov, L., Park, J. (eds) Birational Geometry, K\"ahler--Einstein Metrics and Degenerations, 2019, Springer Proceedings in Mathematics \& Statistics, vol 409, page 195--203 In this short note, we give an alternative proof of the semipositivity of the Chow-Mumford line bundle for families of K-semistable log-Fano pairs, and of the nefness threeshold for the log-anti-canonical line bundle on families of K-stable log Fano pairs. We also prove a bound on the multiplicity of fibers for families of K-semistable log Fano varieties, which to the best of our knowledge is new.
DOI:10.48550/arxiv.2107.07902