A Residue formula and applications to stable sets of foliations

Severine Biard (UPHF)

Nov 20. 2023, 11:00 — 11:50

We will talk about a formula computing the first Chern class of a line bundle in terms of residues of a given connection. This localization formula unifies two results on stable sets of holomorphic foliations of codimension 1. The first result is a positive answer to Brunella's conjecture, stating that every leaf of such a foliation with ample normal bundle in compact complex manifolds of dimension ≥ 3, accumulates on singularities of the foliation. The second result states the non-existence of real analytic Levi-flat hypersurface whose Levi foliation is transversally affine and of 1-convex complement in compact Kähler surfaces. This is a joint work with Masanori Adachi et Judith Brinkschulte.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Analysis and Geometry in Several Complex Variables (Workshop)
Organizer(s):
Peter Ebenfelt (UC San Diego)
Purvi Gupta (IIS Bengalore)
Bernhard Lamel (U of Vienna)
Nordine Mir (Texas A&M U at Qatar)