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October, 2007 Reduction of generalized Calabi-Yau structures
Yasufumi NITTA
J. Math. Soc. Japan 59(4): 1179-1198 (October, 2007). DOI: 10.2969/jmsj/05941179


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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Yasufumi NITTA. "Reduction of generalized Calabi-Yau structures." J. Math. Soc. Japan 59 (4) 1179 - 1198, October, 2007.


Published: October, 2007
First available in Project Euclid: 10 December 2007

zbMATH: 1186.37064
MathSciNet: MR2370010
Digital Object Identifier: 10.2969/jmsj/05941179

Primary: 37J15
Secondary: 14J32

Keywords: Bergman kernels , generalized Calabi-Yau structures , moment maps , the Duistermaat-Heckman formula

Rights: Copyright © 2007 Mathematical Society of Japan


Vol.59 • No. 4 • October, 2007
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