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Singular cscK metrics on smoothable varieties

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arxiv 2312.13653 v3 pith:ISQYUKGV submitted 2023-12-21 math.CV math.AGmath.APmath.DG

Chung-Ming Pan , Tat Dat Tô , Antonio Trusiani This is my paper · ORCID
classification math.CVmath.AGmath.APmath.DG
keywords csckmetricsvarietiesfunctionalmabuchisingularsmoothableahler
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abstract

We prove the lower semi-continuity of the coercivity threshold of Mabuchi functional along a degenerate family of normal compact K\"ahler varieties with klt singularities. Moreover, we establish the existence of singular cscK metrics on $\mathbb{Q}$-Gorenstein smoothable klt varieties when the Mabuchi functional is coercive, these arise as a limit of cscK metrics on close-by fibres. The proof relies on developing a novel strong topology of pluripotential theory in families and establishing uniform estimates for cscK metrics.

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  1. On K\"ahler-Einstein Currents

    math.DG 2025-02 conditional novelty 8.0 of 10

    Singular Kähler-Einstein metrics on klt pairs define Kähler currents, and a tame approximation with L^p Ricci control suffices to make the metric completion an RCD space.

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