Abstract
Following Suwa, we study unfoldings of algebraic foliations and their relationship with families of foliations, making focus on those unfoldings related to trivial families. The results obtained in the study of unfoldings are then applied to obtain information on the structure of foliations on projective spaces.
Similar content being viewed by others
References
Camacho, C., Neto, A.L., Sad, P.: Foliations with algebraic limit sets. Ann. Math. 136(2), 429–446 (1992)
Cerveau, D., Mattéi, J.F.: Formes intégrables holomorphes singulières. Société Mathématique de France (1982)
Gómez-Mont, X.: Unfoldings of holomorphic foliations. Publicacions Matemàtiques. 33(3), 501–515 (1989)
Loray, F., Pereira, J.V., Touzet, F.: Singular foliations with trivial canonical class (2011, preprint). arXiv:1107.1538
Mattei, J.-F.: Modules de feuilletages holomorphes singuliers: I équisingularité. Inventiones mathematicae 103(1), 297–325 (1991)
Quallbrunn, F.: Families of distributions and Pfaff systems under duality. J. Singul. 11(2015), 164–189 (2015). arXiv:1305.3817
Suwa, T.: A theorem of versality for unfoldings of complex analytic foliation singularities. Inventiones mathematicae 65(1), 29–48 (1981)
Suwa, T.: Unfoldings of complex analytic foliations with singularities. Jpn. J. Math. New Ser. 9(1), 181–206 (1983)
Suwa, T.: Structure of the singular set of a complex analytic foliation. Preprint series in mathematics, vol. 33. Hokkaido University (1988)
Suwa, T.: Unfoldings of codimension one complex analytic foliation singularities. Preprint series in mathematics, vol. 173. Hokkaido University (1992)
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Quallbrunn, F. Isotrivial Unfoldings and Structural Theorems for Foliations on Projective Spaces. Bull Braz Math Soc, New Series 48, 335–345 (2017). https://doi.org/10.1007/s00574-016-0024-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00574-016-0024-6