Document type
ArticleVersion
Published versionPublication date
Publication license
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/208001
Classification of the invariants of foliations by curves of low degree on the three-dimensional projective space
Journal Title
Director/Tutor
Journal ISSN
Volume Title
Related resource
Abstract
We study foliations by curves on the three-dimensional projective space with no isolated singularities, which is equivalent to assuming that the conormal sheaf is locally free. We provide a classification of the topological and algebraic invariants of the conormal sheaves and singular schemes for such foliations by curves, up to degree 3. In particular, we prove that foliations by curves of degree 1 or 2 are contained in a pencil of planes or are Legendrian, and are given by the complete intersection of two codimension one distributions. Furthermore, we prove that the conormal sheaf of a foliation by curves of degree 3 with reduced singular scheme either splits as a sum of line bundles or is an instanton bundle. For degree larger than 3, we focus on two classes of foliations by curves, namely Legendrian foliations and those whose conormal sheaf is a twisted null-correlation bundle. We give characterizations of such foliations, describe their singular schemes and their moduli spaces.
Citation
Citation
CORRÊA, Maurício, JARDIM, Marcos and MARCHESI, Simone. Classification of the invariants of foliations by curves of low degree on the three-dimensional projective space. Revista Matematica Iberoamericana. 2023. Vol. 39, num. 5, pags. 1641-1680. ISSN 0213-2230. [consulted: 8 of June of 2026]. Available at: https://hdl.handle.net/2445/208001