Transversely projective structures on smooth foliations on surfaces
Complex Variables
2025-07-08 v2
Abstract
Brunella's classification implies that every smooth foliation on a compact complex surface admits a singular transversely projective structure. However, Biswas and Dumitrescu's recent work shows that certain foliations on compact complex surfaces, despite possessing a singular transversely projective structure, do not admit a regular transversely projective structure. Here, we describe the smooth foliations on compact complex surfaces which fail to possess a regular transversely projective structure.
Cite
@article{arxiv.2405.02273,
title = {Transversely projective structures on smooth foliations on surfaces},
author = {Gabriel Fazoli and Caio Melo and Jorge Vitório Pereira},
journal= {arXiv preprint arXiv:2405.02273},
year = {2025}
}