Kähler--Einstein metrics on quasi-projective manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916708059447296 |
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| author | Dang, Quang-Tuan Vu, Duc-Viet |
| author_facet | Dang, Quang-Tuan Vu, Duc-Viet |
| contents | Let $X$ be a compact Kähler manifold and $D$ be a simple normal crossing divisor on $X$ such that $K_X+D$ is big and nef. We first prove that the singular Kähler--Einstein metric constructed by Berman--Guenancia is almost-complete on $X \backslash D$ in the sense of Tian--Yau. In our second main result, we establish the weak convergence of conic Kähler--Einstein metrics of negative curvature to the above-mentioned metric when $K_X+D$ is merely big, answering partly a recent question posed by Biquard--Guenancia. Potentials of low energy play an important role in our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03858 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kähler--Einstein metrics on quasi-projective manifolds Dang, Quang-Tuan Vu, Duc-Viet Differential Geometry Complex Variables 32U15, 32Q15 Let $X$ be a compact Kähler manifold and $D$ be a simple normal crossing divisor on $X$ such that $K_X+D$ is big and nef. We first prove that the singular Kähler--Einstein metric constructed by Berman--Guenancia is almost-complete on $X \backslash D$ in the sense of Tian--Yau. In our second main result, we establish the weak convergence of conic Kähler--Einstein metrics of negative curvature to the above-mentioned metric when $K_X+D$ is merely big, answering partly a recent question posed by Biquard--Guenancia. Potentials of low energy play an important role in our approach. |
| title | Kähler--Einstein metrics on quasi-projective manifolds |
| topic | Differential Geometry Complex Variables 32U15, 32Q15 |
| url | https://arxiv.org/abs/2309.03858 |