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

Giulio Codogni; Zsolt Patakfalvi

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arXiv · 2107.07902

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

Giulio Codogni·Zsolt Patakfalvi

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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.

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Giulio Codogni, Zsolt Patakfalvi. 2021-07-16. A note on families of K-semistable log-Fano pairs. https://arxiv.org/abs/2107.07902

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