Variation of Hodge structure for generalized complex manifolds

Abstract

A generalized complex manifold which satisfies the $\partial \overline{\partial}$-lemma admits a Hodge decomposition in twisted cohomology. Using a Courant algebroid theoretic approach we study the behavior of the Hodge decomposition in smooth and holomorphic families of generalized complex manifolds. In particular we define period maps, prove a Griffiths transversality theorem and show that for holomorphic families the period maps are holomorphic. Further results on the Hodge decomposition for various special cases including the generalized K\"ahler case are obtained.Comment: 38 page

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“…2.1 广义 Hermite 流形 本小节介绍紧致广义 Hermite 流形的基本定义和性质, 具体内容可参见文献 [3][4][5][6][7]. 首先, 设 X 2n 为一个光滑流形, 其实维数为 dim R X = 2n.…”

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“…Let (M, J) be a compact H-twisted generalized Calabi-Yau manifold. Then there exists a globally L 2 convergent power series which determines the deformation in t < 1 4ac , (t)ρ 0 =…”

On generalized Kähler geometry on compact Lie groups

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