The logarithmic leaf complex and foliated d-semistability
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910183247052800 |
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| author | Corrêa, Mauricio Perrella, Pablo Velazquez, Sebastián |
| author_facet | Corrêa, Mauricio Perrella, Pablo Velazquez, Sebastián |
| contents | We study holomorphic foliations on normal crossings varieties arising as semistable degenerations. We do so by we exploring the notion of foliated d-semistability using the language of logarithmic structures in the sense of Fontaine-Illusie. First, we identify both local and global obstructions to d-semistability. In order to analyze the existence of smoothings, we develop a logarithmic deformation theory of foliations and show that the corresponding moduli functor admits a versal hull. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00285 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The logarithmic leaf complex and foliated d-semistability Corrêa, Mauricio Perrella, Pablo Velazquez, Sebastián Algebraic Geometry 14D15, 37F75, 14D20 We study holomorphic foliations on normal crossings varieties arising as semistable degenerations. We do so by we exploring the notion of foliated d-semistability using the language of logarithmic structures in the sense of Fontaine-Illusie. First, we identify both local and global obstructions to d-semistability. In order to analyze the existence of smoothings, we develop a logarithmic deformation theory of foliations and show that the corresponding moduli functor admits a versal hull. |
| title | The logarithmic leaf complex and foliated d-semistability |
| topic | Algebraic Geometry 14D15, 37F75, 14D20 |
| url | https://arxiv.org/abs/2605.00285 |