Understand
Generalized Kahler geometry is the natural analogue of Kahler geometry, in the context of generalized complex geometry.
- Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible with a metric so that it defines a second generalized complex structure.
- We explore the fundamental aspects of this geometry, including its equivalence with the bi-Hermitian geometry on the target of a 2-dimensional sigma model with (2,2) supersymmetry, as well as the relation to holomorphic Dirac geometry and the resulting derived deformation theory.
- We also explore the analogy between pre-quantum line bundles and gerbes in the context of generalized Kahler geometry.