English

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}
}
R2 v1 2026-06-28T16:15:51.269Z