Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variation of Hodge structure for generalized complex manifolds   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.

27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph