Picard groups of completed period images and the Deng-Robles problem
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911503235416064 |
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| author | Mounda, Badre Zheng, Dongzhe |
| author_facet | Mounda, Badre Zheng, Dongzhe |
| contents | A basic problem in the geometry of degenerating period maps is to determine whether their completed images admit an intrinsic algebraic description. For polarized variations of Hodge structure over smooth quasi-projective surfaces, Deng and Robles formulated such a problem in terms of the Kato-Nakayama-Usui completion of the period image and a conjectural Proj description involving the augmented Hodge line bundle and the boundary divisor on a smooth compactification of the base. We show that the essential obstruction to this description is divisor-theoretic: it may be expressed as a Picard-generation statement on the completed mixed period image. We prove this statement when the pure period image is one-dimensional, and consequently obtain the Deng-Robles Proj description in this case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09709 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Picard groups of completed period images and the Deng-Robles problem Mounda, Badre Zheng, Dongzhe Algebraic Geometry 14D07, 32G20, 14C20 A basic problem in the geometry of degenerating period maps is to determine whether their completed images admit an intrinsic algebraic description. For polarized variations of Hodge structure over smooth quasi-projective surfaces, Deng and Robles formulated such a problem in terms of the Kato-Nakayama-Usui completion of the period image and a conjectural Proj description involving the augmented Hodge line bundle and the boundary divisor on a smooth compactification of the base. We show that the essential obstruction to this description is divisor-theoretic: it may be expressed as a Picard-generation statement on the completed mixed period image. We prove this statement when the pure period image is one-dimensional, and consequently obtain the Deng-Robles Proj description in this case. |
| title | Picard groups of completed period images and the Deng-Robles problem |
| topic | Algebraic Geometry 14D07, 32G20, 14C20 |
| url | https://arxiv.org/abs/2603.09709 |