Foliations on \mathbbCP³ of degree 2 that have a line as singular set

2022/12/19 by Alcántara, Claudia R., Cerveau, Dominique
#32M25 #32S65 #37F75 (primary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.09845

Abstract

In this work we classify foliations on \mathbbCP³ of codimension 1 and degree 2 that have a line as singular set. To achieve this, we do a complete description of the components. We prove that the boundary of the exceptional component has only 3 foliations up to change of coordinates, and this boundary is contained in a logarithmic component. Finally we construct examples of foliations on \mathbbCP³ of codimension 1 and degree s ≥ 3 that have a line as singular set and such that they form a family with a rational first integral of degree s+1 or they are logarithmic foliations where some of them have a minimal rational first integral of degree not bounded.

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