B-complex manifolds with generalized corners. I. Newlander-Nirenberg Theorems

Preprint

We generalize complex manifolds to manifolds with corners $X$, and to manifolds with generalized corners (g-corners) in the sense of the second author https://arxiv.org/abs/1501.00401, using complex structures on the b-tangent bundle (log tangent bundle) ${}^b TX$. 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~\cite{1} we show that if $S$ is a log smooth log $C$-scheme, or log smooth log complex analytic space, then the Kato-Nakayama space $S^{\mathrm{KN}}$ 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.

Authors: Arguz, H; Joyce, D

• Publication status: Published
• Peer review status: Not peer reviewed
• Preprint server: arXiv
• Publication date: 2026-04-24
• DOI: 10.48550/arXiv.2604.22642
• EISSN: 2331-8422
• Language: English