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Codimension one foliations of degree three on projective spaces

2021; Elsevier BV; Volume: 174; Linguagem: Inglês

10.1016/j.bulsci.2021.103092

1952-4773

Raphael Constant da Costa, Ruben Lizarbe, Jorge Vitório Pereira,

Geometric Analysis and Curvature Flows

We establish a structure theorem for degree three codimension one foliations on projective spaces of dimension n≥3, extending a result by Loray, Pereira, and Touzet for degree three foliations on P3. We show that the space of codimension one foliations of degree three on Pn, n≥3, has exactly 18 distinct irreducible components parameterizing foliations without rational first integrals, and at least 6 distinct irreducible components parameterizing foliations with rational first integrals.