Linear pencils of foliations over \(\mathbb{C}\mathbb{P}(3)\) and Brunella's conjecture
The conjecture of Brunella states that if \(\mathcal F\) is a holomorphic foliation of codimension one on \(\mathbb{C} P(3)\), then either \(\mathcal F\) has an invariant surface or there exists a (singular) holomorphic foliation \(\mathcal G\) whose leaves are Riemann surfaces which are contained in those ones of \(\mathcal F\) and their closures are algebraic. The author shows that this conjecture holds for a generic element of a linear pencil of codimension one foliations of degree \( \nu \) . A very interesting discussion on the conjecture, its relations with other results and on generalisations to higher dimensions is also presented.
scientific article; zbMATH DE number 1876878