• Lecturer: Judith Brinkschulte
• Date: Tuesday 11:15 - 12:45
• Room: Leipzig University, Augusteum, room A-314
• Language: English
• Target audience: MSc students, PhD students, Postdocs
• Keywords: Complex geometry, complex analysis
• Prerequisites: Analysis, basic knowledge of differential geometry and functional analysis

Abstract

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.