Recent Results on Equivalence of Neighborhoods of Embedded Compact Complex Manifolds and Higher-Codimension Foliations

par Laurent Stolovitch

vendredi 16 oct. 2026, 14:00 → 15:00 Europe/Paris

Amphi TURING

In this talk, we will survey recent works done in collaboration
with Xianghong Gong, Takayuki Koike, Xiaojun Wu. We consider an embedded
n-dimensional compact complex manifold C in n+d- dimensional complex
manifolds. We are interested in the holomorphic classification of
neighborhoods when the normal bundle is flat.

We will give conditions ensuring that a neighborhood of C in M is
biholomorphic to a neighborhood of the zero section of its normal bundle.
We also give conditions ensuring the existence of a holomorphic foliation in
a neighborhood of C in M having C as a compact leaf, extending Ueda's theory to the higher dimension and codimension cases. Both problems appear as a kind "linearization problem" involving apprioriate notions of {\ir
resonances} and  {\it small divisors condition}.