Singular cscK metrics on smoothable varieties
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866915349163671552 |
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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 |