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Abstract: Generalized Kahler geometry is the natural analogue of Kahler geometry, inthe context of generalized complex geometry. Just as we may require a complexstructure to be compatible with a Riemannian metric in a way which gives riseto a symplectic form, we may require a generalized complex structure to becompatible with a metric so that it defines a second generalized complexstructure. We explore the fundamental aspects of this geometry, including itsequivalence with the bi-Hermitian geometry on the target of a 2-dimensionalsigma model with 2,2 supersymmetry, as well as the relation to holomorphicDirac geometry and the resulting derived deformation theory. We also explorethe analogy between pre-quantum line bundles and gerbes in the context ofgeneralized Kahler geometry.

Author: Marco Gualtieri


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