English

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}
}
R2 v1 2026-07-01T12:44:36.310Z