2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126177A 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.14 pages, to appear in J. Math. Soc. Japan, Vol 59, no. 4(2007)Differential GeometrySymplectic Geometry37J15; 14J32text