An iterative construction of complete Kähler--Einstein metrics
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912815416082432 |
|---|---|
| author | Dang, Quang-Tuan Tô, Tat Dat |
| author_facet | Dang, Quang-Tuan Tô, Tat Dat |
| contents | We extend Tsuji's iterative construction of complete Kähler--Einstein metrics with negative scalar curvature to noncompact Kähler manifolds with bounded geometry, using Berndtsson's method from the compact setting. Consequently, given a holomorphic surjective map $p:X\to Y$, where $X$ is a weakly pseudoconvex Kähler manifold and $Y$ is a complex manifold, and where the smooth fibers admit Kähler--Einstein metrics with negative scalar curvature and bounded geometry, we show that the fiberwise Kähler--Einstein metrics induce a semipositively curved metric on the relative canonical bundle $K_{X/Y}$. Moreover, our approach also applies to the plurisubharmonic variation of cusp Kähler--Einstein metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12599 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An iterative construction of complete Kähler--Einstein metrics Dang, Quang-Tuan Tô, Tat Dat Differential Geometry Complex Variables 32U15, 32Q15, 32W20 We extend Tsuji's iterative construction of complete Kähler--Einstein metrics with negative scalar curvature to noncompact Kähler manifolds with bounded geometry, using Berndtsson's method from the compact setting. Consequently, given a holomorphic surjective map $p:X\to Y$, where $X$ is a weakly pseudoconvex Kähler manifold and $Y$ is a complex manifold, and where the smooth fibers admit Kähler--Einstein metrics with negative scalar curvature and bounded geometry, we show that the fiberwise Kähler--Einstein metrics induce a semipositively curved metric on the relative canonical bundle $K_{X/Y}$. Moreover, our approach also applies to the plurisubharmonic variation of cusp Kähler--Einstein metrics. |
| title | An iterative construction of complete Kähler--Einstein metrics |
| topic | Differential Geometry Complex Variables 32U15, 32Q15, 32W20 |
| url | https://arxiv.org/abs/2410.12599 |