Singular cscK metrics on smoothable varieties

Chung-Ming Pan; Tat Dat Tô; Antonio Trusiani

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arXiv · 2312.13653

Singular cscK metrics on smoothable varieties

Chung-Ming Pan·Tat Dat Tô·Antonio Trusiani

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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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BibTeX RIS

Chung-Ming Pan, Tat Dat Tô, Antonio Trusiani. 2023-12-21. Singular cscK metrics on smoothable varieties. https://arxiv.org/abs/2312.13653

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