Reduction of Courant algebroids and generalized complex structures
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We present a theory of reduction for Courant algebroids as well as Dirac structures, generalized complex, and generalized Kähler structures which interpolates between holomorphic reduction of complex manifolds and symplectic reduction. The enhanced symmetry group of a Courant algebroid leads us to define \emph{extended} actions and a generalized notion of moment map. Key examples of generalized Kähler reduced spaces include new explicit bi-Hermitian metrics on $\CC P^2$.
34 pages. Presentation greatly improved, one subsection added, errors corrected, references added. v3: a few changes in the presentation, material slightly reorganized, final version to appear in Adv. in Math
34 pages. Presentation greatly improved, one subsection added, errors corrected, references added. v3: a few changes in the presentation, material slightly reorganized, final version to appear in Adv. in Math