Toric geometry of generalized Kähler-Ricci solitons
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866914018370781184 |
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| author | Apostolov, Vestislav Barbaro, Giuseppe Streets, Jeffrey Ustinovskiy, Yury |
| author_facet | Apostolov, Vestislav Barbaro, Giuseppe Streets, Jeffrey Ustinovskiy, Yury |
| contents | We establish a local equivalence between toric steady Kähler-Ricci solitons and $A$-type toric generalized Kähler-Ricci solitons (GKRS). Under natural global conditions we show this equivalence extends to complete GKRS, yielding a general construction of new examples in all dimensions. We show that in four dimensions, all GKRS are either described by the generalized Kähler Gibbons-Hawking ansatz, or have split tangent bundle, or are $A$-type toric. This yields a local classification in four dimensions, together with a conjecturally exhaustive construction of complete symplectic-type examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01639 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Toric geometry of generalized Kähler-Ricci solitons Apostolov, Vestislav Barbaro, Giuseppe Streets, Jeffrey Ustinovskiy, Yury Differential Geometry Complex Variables We establish a local equivalence between toric steady Kähler-Ricci solitons and $A$-type toric generalized Kähler-Ricci solitons (GKRS). Under natural global conditions we show this equivalence extends to complete GKRS, yielding a general construction of new examples in all dimensions. We show that in four dimensions, all GKRS are either described by the generalized Kähler Gibbons-Hawking ansatz, or have split tangent bundle, or are $A$-type toric. This yields a local classification in four dimensions, together with a conjecturally exhaustive construction of complete symplectic-type examples. |
| title | Toric geometry of generalized Kähler-Ricci solitons |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2509.01639 |