In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers.

Complex geometry is on the crossroad of algebraic and differential geometry. Complex geometry is also becoming a stimulating and useful tool for theoretical physicists working in string theory and …

August 23, 2023 These are lecture notes from the Fall 2020 course M392C Complex Geometry at the University of Texas at Austin taught by Prof. Bernd Seibert. The prerequisites for following these …

Contents: The primary goal of this Module is to present some fundamental techniques from several complex variables, Hermitian di erential geometry (and partial di erential equations, potential theory, …

In the following section, we will learn about complex manifolds/varieties, complex submanifolds/subvarieties, and holomorphic vector bundles. In particular, we will be interested in …

The aims of the course were to introduce bright students, most of whom were freshmen, to complex numbers in a friendly, elegant fashion and to develop reasoning skills belonging to the realm of …

A complex manifold is a diferentiable manifold of even real dimension equipped with a complex structure: there exists a covering by open sets, which are difeomorphic to open sets of Cn, such that …