Seminar: Josias Reppekus (Hörsaal 2, BZ.08.04)
Thursday 30.06.2022 at 16:15 in Hörsaal 2 (BZ.08.04) I will give (Part 1 of) a talk on
Convexity of Complements of Limit Sets for Holomorphic Foliations on Surfaces
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.