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Some criteria for uniform K-stability

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arxiv 1907.05293 v1 pith:FGPP55KY submitted 2019-07-11 math.AG math.DG

Chuyu Zhou , Ziquan Zhuang This is my paper · ORCID
classification math.AGmath.DG
keywords k-stabilityuniformcriteriasomebetaboundconjecturalconjecture
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abstract

We prove some criteria for uniform K-stability of log Fano pairs. In particular, we show that uniform K-stability is equivalent to $\beta$-invariant having a positive lower bound. Then we study the relation between optimal destabilization conjecture and the conjectural equivalence between uniform K-stability and K-stability in the twisted setting.

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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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