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Openness of K-semistability for Fano varieties

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arxiv 1907.02408 v3 pith:WRU33AFC submitted 2019-07-04 math.AG math.DG

Harold Blum , Yuchen Liu , Chenyang Xu This is my paper · ORCID
classification math.AGmath.DG
keywords fanok-semistabilityopennessprovestabilitythresholdarisesbounded
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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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  1. Analytic Bertini theorem II --- The local case

    math.AG 2026-07 accept novelty 8.0 of 10

    The local analytic Bertini theorem holds: multiplier ideal sheaves of psh functions on polydisc products restrict to fibers outside a pluripolar set.

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