SNC Kähler-Einstein metrics and RCD spaces
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912849993924608 |
|---|---|
| author | de Borbon, Martin Spotti, Cristiano |
| author_facet | de Borbon, Martin Spotti, Cristiano |
| contents | We show that Kähler-Einstein metrics with cone singularities along simple normal crossing (SNC) divisors define RCD spaces, both in the compact setting and in certain non-compact cases, thereby producing many examples of Einstein RCD spaces. In particular, we show the existence of smooth non-compact $4$-manifolds carrying ALE Ricci-flat RCD$(0,4)$ metrics with any space form $S^3/Γ$ as the link of the tangent cone at infinity, answering a question raised by D. Semola. Our proofs rely on the characterization of RCD spaces in the almost-smooth setting due to S. Honda and Honda-Sun. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18741 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | SNC Kähler-Einstein metrics and RCD spaces de Borbon, Martin Spotti, Cristiano Differential Geometry We show that Kähler-Einstein metrics with cone singularities along simple normal crossing (SNC) divisors define RCD spaces, both in the compact setting and in certain non-compact cases, thereby producing many examples of Einstein RCD spaces. In particular, we show the existence of smooth non-compact $4$-manifolds carrying ALE Ricci-flat RCD$(0,4)$ metrics with any space form $S^3/Γ$ as the link of the tangent cone at infinity, answering a question raised by D. Semola. Our proofs rely on the characterization of RCD spaces in the almost-smooth setting due to S. Honda and Honda-Sun. |
| title | SNC Kähler-Einstein metrics and RCD spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2601.18741 |