Embedding theorems in complex geometry

The aim of this lecture is to discuss well-known and important embedding theorems in complex geometry. The starting point is Kodaira's embedding theorem which asserts that a compact complex manifold admitting a positive line bundle admits a holomorphic embedding into some complex projective space. I will present a proof relying on vanishing theorems for \(\overline\partial\)-cohomology groups. I will then discuss generalizations leading to characterizations of Moishezon manifolds.

Using similar methods, I will discuss holomorphic embeddings of Stein manifolds into Euclidean spaces. I will also review historical and recent results on the minimal embedding and immersion dimensions.

Date and time info
Tuesday 11:15 - 12:45

Keywords
Complex geometry, complex analysis

Prerequisites
Analysis, basic knowledge of differential geometry and functional analysis

Audience
MSc students, PhD students, Postdocs

Language
English