From amoebas to pluripotential theory on hybrid analytic spaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909851879211008 |
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| author | Boucksom, Sebastien |
| author_facet | Boucksom, Sebastien |
| contents | These lecture notes are an introduction to the use of non-Archimedean geometry in the study of meromorphic degenerations of complex algebraic varieties. They provide a self-contained discussion of hybrid spaces, which fill in one-parameter degenerations with the associated non-Archimedean Berkovich space as a central fiber. The main focus is on the interplay between complex and non-Archimedean pluripotential theory, and on the relation between convergence of psh metrics and the associated Monge-Ampere measures in the hybrid space, following work of the author with M.Jonsson, and recent breakthrough work by Y.Li. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10239 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From amoebas to pluripotential theory on hybrid analytic spaces Boucksom, Sebastien Algebraic Geometry Complex Variables Differential Geometry 32Q26 These lecture notes are an introduction to the use of non-Archimedean geometry in the study of meromorphic degenerations of complex algebraic varieties. They provide a self-contained discussion of hybrid spaces, which fill in one-parameter degenerations with the associated non-Archimedean Berkovich space as a central fiber. The main focus is on the interplay between complex and non-Archimedean pluripotential theory, and on the relation between convergence of psh metrics and the associated Monge-Ampere measures in the hybrid space, following work of the author with M.Jonsson, and recent breakthrough work by Y.Li. |
| title | From amoebas to pluripotential theory on hybrid analytic spaces |
| topic | Algebraic Geometry Complex Variables Differential Geometry 32Q26 |
| url | https://arxiv.org/abs/2510.10239 |