The logarithmic leaf complex and foliated d-semistability
Algebraic Geometry
2026-05-04 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2605.00285,
title = {The logarithmic leaf complex and foliated d-semistability},
author = {Mauricio Corrêa and Pablo Perrella and Sebastián Velazquez},
journal= {arXiv preprint arXiv:2605.00285},
year = {2026}
}