Complex Differential Geometry

This course will introduce Complex Differential Geometry, a geometry based on complex analysis of several complex variables. The main sort of space in this geometry is Complex Manifolds. We will cover their basic theory using sheaf theory and hermitian differential geometric concepts such as connections and curvature with emphasis on Compact Complex Manifolds. The goal is to treat the Dolebeault and De Rham theorems, the Hodge theorem on harmonic integrals and the Kodaira embedding theorem.