Algebraic geometry of bubbling Kahler metrics
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910835232735232 |
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| author | Odaka, Yuji |
| author_facet | Odaka, Yuji |
| contents | We give an algebro-geometric or non-archimedean framework to study bubbling phenomena of Kahler metrics with Euclidean volume growth, after [DS17, Sun23, dBS23]. In particular, for any degenerating family to log terminal singularity, we algebraically construct a finite sequence of birational modifications of the family with milder degenerations, and compare with analytic bubbling constructions in loc.cit. We also provide approaches in terms of coordinates and valuations. Our discussion partially depends on the general framework of stability theory in our [Od24b] (arXiv:2406.02489) after [HL14, AHLH23]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14518 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic geometry of bubbling Kahler metrics Odaka, Yuji Algebraic Geometry High Energy Physics - Theory Differential Geometry We give an algebro-geometric or non-archimedean framework to study bubbling phenomena of Kahler metrics with Euclidean volume growth, after [DS17, Sun23, dBS23]. In particular, for any degenerating family to log terminal singularity, we algebraically construct a finite sequence of birational modifications of the family with milder degenerations, and compare with analytic bubbling constructions in loc.cit. We also provide approaches in terms of coordinates and valuations. Our discussion partially depends on the general framework of stability theory in our [Od24b] (arXiv:2406.02489) after [HL14, AHLH23]. |
| title | Algebraic geometry of bubbling Kahler metrics |
| topic | Algebraic Geometry High Energy Physics - Theory Differential Geometry |
| url | https://arxiv.org/abs/2406.14518 |