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arXiv · 2405.02273

Transversely projective structures on smooth foliations on surfaces

Gabriel Fazoli·Caio Melo·Jorge Vitório Pereira
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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.

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Gabriel Fazoli, Caio Melo, Jorge Vitório Pereira. 2024-05-03. Transversely projective structures on smooth foliations on surfaces. https://doi.org/10.1007/s00229-025-01643-w

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