Combinatorics and Hodge theory of degenerations of abelian varieties: A survey of the Mumford construction
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910077253844992 |
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| author | Engel, Philip Fortman, Olivier de Gaay Schreieder, Stefan |
| author_facet | Engel, Philip Fortman, Olivier de Gaay Schreieder, Stefan |
| contents | We survey the Mumford construction of degenerating abelian varieties, with a focus on the analytic version of the construction, and its relation to toric geometry. Moreover, we study the geometry and Hodge theory of multivariable degenerations of abelian varieties associated to regular matroids, and extend some fundamental results of Clemens on 1-parameter semistable degenerations to the multivariable setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15695 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Combinatorics and Hodge theory of degenerations of abelian varieties: A survey of the Mumford construction Engel, Philip Fortman, Olivier de Gaay Schreieder, Stefan Algebraic Geometry Complex Variables 14K10, 14K25, 14C30, 05B35, 32G20, 14M25 We survey the Mumford construction of degenerating abelian varieties, with a focus on the analytic version of the construction, and its relation to toric geometry. Moreover, we study the geometry and Hodge theory of multivariable degenerations of abelian varieties associated to regular matroids, and extend some fundamental results of Clemens on 1-parameter semistable degenerations to the multivariable setting. |
| title | Combinatorics and Hodge theory of degenerations of abelian varieties: A survey of the Mumford construction |
| topic | Algebraic Geometry Complex Variables 14K10, 14K25, 14C30, 05B35, 32G20, 14M25 |
| url | https://arxiv.org/abs/2507.15695 |