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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.22642 |
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| _version_ | 1866918466443804672 |
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| author | Argüz, Hülya Joyce, Dominic |
| author_facet | Argüz, Hülya Joyce, Dominic |
| contents | We generalize complex manifolds to manifolds with corners $X$, and to manifolds with generalized corners (g-corners) in the sense of the second author arXiv:1501.00401, using complex structures on the b-tangent bundle (log tangent bundle) ${}^bTX$. We prove a formal Newlander-Nirenberg type theorem showing that along each corner stratum of $X$, the b-complex structure agrees with a standard model to infinite order.
In the sequel we show that if $S$ is a log smooth log $\mathbb C$-scheme, or log smooth log complex analytic space, then the Kato-Nakayama space $S^{\rm KN}$ has the structure of a b-complex manifold with g-corners. Using our Newlander-Nirenberg theorem we give necessary and sufficient conditions for a b-complex manifold with g-corners to be a Kato-Nakayama space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22642 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | B-complex manifolds with generalized corners. I. Newlander-Nirenberg Theorems Argüz, Hülya Joyce, Dominic Differential Geometry Algebraic Geometry We generalize complex manifolds to manifolds with corners $X$, and to manifolds with generalized corners (g-corners) in the sense of the second author arXiv:1501.00401, using complex structures on the b-tangent bundle (log tangent bundle) ${}^bTX$. We prove a formal Newlander-Nirenberg type theorem showing that along each corner stratum of $X$, the b-complex structure agrees with a standard model to infinite order. In the sequel we show that if $S$ is a log smooth log $\mathbb C$-scheme, or log smooth log complex analytic space, then the Kato-Nakayama space $S^{\rm KN}$ has the structure of a b-complex manifold with g-corners. Using our Newlander-Nirenberg theorem we give necessary and sufficient conditions for a b-complex manifold with g-corners to be a Kato-Nakayama space. |
| title | B-complex manifolds with generalized corners. I. Newlander-Nirenberg Theorems |
| topic | Differential Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2604.22642 |