GdT Komplex

Introduction to the Exceptional minimal set problem

by Prof. Julio Rebelo (IMT)

Pelos (IMT)




The exceptional minimal set conjecture states that every leaf of a holomorphic foliation on the complex projective plane must accumulate at singular points. In this sense, the conjecture can be seen as an analogue of the well-known Poincare-Bendixson theorem on (real) vector fields defined on the sphere $S^2$. In this talk, we will discuss some general properties of these minimal sets, if they ever exist, and comment on some approaches that have been designed to prove the conjecture.