Reduction of generalized Calabi-Yau structures

Details Reduction of generalized Calabi-Yau structures Reduction of generalized Calabi-Yau structures

2006-11-12

arxiv.org/abs/math/0611341v2

Mathematics

Differential Geometry

14 pages, to appear in J. Math. Soc. Japan, Vol 59, no. 4(2007)

Scientific paper

A generalized Calabi-Yau structure is a geometrical structure on a manifold which generalizes both the concept of the Calabi-Yau structure and that of the symplectic one. In view of a result of Lin and Tolman in generalized complex cases, we introduce in this paper the notion of a generalized moment map for a compact Lie group action on a generalized Calabi-Yau manifold and construct a reduced generalized Calabi-Yau structure on the reduced space. As an application, we show some relationship between generalized moment maps and the Bergman kernels, and prove the Duistermaat-Heckman formula for a torus action on a generalized Calabi-Yau manifold.

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