MIT MIT-OCW
Topics in Several Complex Variables
A graduate-level MIT OpenCourseWare course on complex analysis in several variables, focused on harmonic theory over complex manifolds. Topics include the Hodge decomposition theorem, the Hard Lefschetz theorem, and vanishing theorems for holomorphic vector bundles, along with tools for studying deformation and uniformization of complex manifolds. Materials consist of MIT's course notes and readings, provided free through OpenCourseWare under a Creative Commons license, with no certificate offered. The course assumes strong prior background in complex analysis and differential geometry, aiming at students working toward research in complex geometry or related areas of mathematics.