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 Kähler case are obtained.

38 pages

References in corpus (5)

• Generalized complex geometry
• New aspects of the ddc-lemma
• Generalized geometry and the Hodge decomposition
• AV-Courant algebroids and generalized CR structures
• On deformations of generalized Calabi-Yau, hyperKähler, $G_2$ and Spin$(7)$ structures I

Cited by in corpus (1)

• Some Results of Deformations on Compact $H$-twisted Generalized Calabi-Yau Manifolds