Fano Fibrations and Twisted Kähler-Einstein Metrics I
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909976248713216 |
|---|---|
| author | Bednarek, Alexander |
| author_facet | Bednarek, Alexander |
| contents | This is the first of two papers studying both the geometric structure of Fano fibrations and the application to Kähler-Ricci flows developing a singularity in finite time. Given a Fano fibration which is generated by Kawamata's theorem from a compact Kähler manifold $X$ endowed with an ample, rational line bundle $L$ and non-nef canonical line bundle $K_X$, we construct a $(1,1)$-form on the regular part of the base analytic variety which is related to the Weil-Petersson metric. It is also proven that the singular Kähler metric constructed by Zhang, Zhang, on the base analytic variety satisfies a twisted Kähler-Einstein equation involving this $(1,1)$-form and, for a submersion, that the Chern classes of $X$ and the base manifold decompose in terms of this $(1,1)$-form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21904 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fano Fibrations and Twisted Kähler-Einstein Metrics I Bednarek, Alexander Differential Geometry Algebraic Geometry Complex Variables 53E30, 14D06, 32W50 This is the first of two papers studying both the geometric structure of Fano fibrations and the application to Kähler-Ricci flows developing a singularity in finite time. Given a Fano fibration which is generated by Kawamata's theorem from a compact Kähler manifold $X$ endowed with an ample, rational line bundle $L$ and non-nef canonical line bundle $K_X$, we construct a $(1,1)$-form on the regular part of the base analytic variety which is related to the Weil-Petersson metric. It is also proven that the singular Kähler metric constructed by Zhang, Zhang, on the base analytic variety satisfies a twisted Kähler-Einstein equation involving this $(1,1)$-form and, for a submersion, that the Chern classes of $X$ and the base manifold decompose in terms of this $(1,1)$-form. |
| title | Fano Fibrations and Twisted Kähler-Einstein Metrics I |
| topic | Differential Geometry Algebraic Geometry Complex Variables 53E30, 14D06, 32W50 |
| url | https://arxiv.org/abs/2512.21904 |