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.
Codogni, G., Patakfalvi, Z. (2023). A note on families of K-semistable log-Fano pairs. In Birational Geometry, Kähler–Einstein Metrics and Degenerations, Conference proceedings (pp.195-203). Springer [10.1007/978-3-031-17859-7_9].
A note on families of K-semistable log-Fano pairs
Codogni, Giulio;
2023-05-23
Abstract
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.| File | Dimensione | Formato | |
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