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arXiv · 1907.02408

Openness of K-semistability for Fano varieties

Harold Blum·Yuchen Liu·Chenyang Xu
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Abstract

In this paper, we prove the openness of K-semistability in families of log Fano pairs by showing that the stability threshold is a constructible function on the fibers. We also prove that any special test configuration arises from a log canonical place of a bounded complement and establish properties of any minimizer of the stability threshold.

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Harold Blum, Yuchen Liu, Chenyang Xu. 2021-10-29. Openness of K-semistability for Fano varieties. https://arxiv.org/abs/1907.02408

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