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Uniform K-stability and asymptotics of energy functionals in K\"ahler geometry

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arxiv 1603.01026 v5 pith:KISHHV52 submitted 2016-03-03 math.DG math.AG

Sébastien Boucksom , Tomoyuki Hisamoto , Mattias Jonsson This is my paper · ORCID
classification math.DGmath.AG
keywords definedahlerconfigurationfunctionalfunctionalsgeometryk-stabilitymetric
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Consider a polarized complex manifold (X,L) and a ray of positive metrics on L defined by a positive metric on a test configuration for (X,L). For most of the common functionals in K\"ahler geometry, we prove that the slope at infinity along the ray is given by evaluating the non-Archimedean version of the functional (as defined in our earlier paper) at the non-Archimedean metric on L defined by the test configuration. Using this asymptotic result, we show that coercivity of the Mabuchi functional implies uniform K-stability.

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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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