Complex geometry - Wikipedia
In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers.
Part 1. Basic Complex Geometry In this part, we mainly follows [Huy05] and [Dem12]. 0. Review of complex analysis 0.1. One variable case. We first give a quick review about basic results in holomorphic functions of one variable. Fix an open subset U C. There are too many ways to define a holomorphic function, and all of them are equivalent.
Complex Geometry: An Introduction | SpringerLink
Complex geometry studies (compact) complex manifolds. It discusses algebraic as well as metric aspects. The subject is on the crossroad of algebraic and differential geometry.
complex geometry. We de ne the exponential function by its power series and the cosine and sine functions by way of the exponential function. We can and therefore do discuss logarithms and trigonometry in this chapter as well. Chapter 3 focuses on geometric aspects of complex numbers. We analyze the
Introduction to complex geometry Yalong Shi Abstract Notes for 2020 BICMR Summer School for Di erential Geometry. Contents 1 Preliminaries in complex analysis 3 2 Complex manifolds and complex...
This section is an introduction to complex geometry. For other references in the style of these notes, see Kodaira’s book [19], Chapter 1 of Siu’s notes [24], Chapter 1 of Song-Weinkove’s notes [25], or
Generalized complex geometry encompasses complex and symplectic ge-ometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group, elliptic deforma-tion theory, relation to Poisson geometry, and local structure theory.
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, functional analysis), to study the geometry of complex, and …
1 Why study complex geometry? The main goal of this course is to understand the natural di erential geometry of complex manifolds: K ahler geometry. Why should we care about this? Several possible answers. For di erential geometers: A general Riemannian metric is a di cult beast. We’d like to
Complex Geometry and Lie Groups
The workshop focuses on research fields in Complex Geometry and Several Complex Variables which have interplay with Lie group and homogeneous space theory. For instance, Cartan Geometry, which places a Lie group and a homogeneous space as a core space, is becoming a standard framework for the study of geometry and analysis of manifolds.