Singular cscK metrics on smoothable varieties

Fuente: arXiv
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Autori principali: Pan, Chung-Ming, Tô, Tat Dat, Trusiani, Antonio
Natura: Preprint
Pubblicazione: 2023
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author Pan, Chung-Ming
Tô, Tat Dat
Trusiani, Antonio
author_facet Pan, Chung-Ming
Tô, Tat Dat
Trusiani, Antonio
contents We prove the lower semi-continuity of the coercivity threshold of Mabuchi functional along a degenerate family of normal compact Kähler 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.
format Preprint
id arxiv_https___arxiv_org_abs_2312_13653
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Singular cscK metrics on smoothable varieties
Pan, Chung-Ming
Tô, Tat Dat
Trusiani, Antonio
Complex Variables
Algebraic Geometry
Analysis of PDEs
Differential Geometry
We prove the lower semi-continuity of the coercivity threshold of Mabuchi functional along a degenerate family of normal compact Kähler 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.
title Singular cscK metrics on smoothable varieties
topic Complex Variables
Algebraic Geometry
Analysis of PDEs
Differential Geometry
url https://arxiv.org/abs/2312.13653