Working Group: Josias Reppekus (BZ.08.04 - Hörsaal 02)
The talk is based on the eponymous paper by Bertrand Deroin, Christophe Dupont and Victor Kleptsyn found here: https://arxiv.org/abs/2202.01007.
For a holomorphic foliation F of a compact Kähler Surface with hyperbolic singularities and no foliation cycles, we prove that if the limit set of F is thin (e.g. has Lebesgue measure 0), then its complement is the modification of a Stein domain. The proof consists in a metric of positive curvature on the normal bundle of F near the limit set. Then we adapt a construction by Brunella to obtain a strictly plurisubharmonic exhaustion function for the complement near the limit set.
