Generalized complex geometry

Abstract

Generalized complex geometry encompasses complex and symplectic geometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group, elliptic deformation theory, relation to Poisson geometry, and local structure theory. We also dene and study generalized complex branes, which interpolate between at bundles on Lagrangian submanifolds and holomorphic bundles on complex submanifolds.