Introduction to Generalized Kahler Geometry I

Explore the foundations of generalized Kähler geometry in this comprehensive lecture. Begin with an examination of the equivalence between generalized Kähler and bihermitian structures, focusing initially on key features in four dimensions before expanding to higher-dimensional contexts. Delve into the connections with holomorphic Poisson geometry and investigate analogues of standard Kähler properties, including the existence of local Kähler potential and stability under small deformations in the generalized setting. Gain valuable insights into this advanced mathematical topic through clear explanations and in-depth analysis.