2012/05/01 by David Baraglia
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Cohomology #Complex manifold #Decomposition #Hodge structure #Hodge theory #Holomorphic function #Homotopy and Cohomology in Algebraic Topology #Identity theorem #Lemma (botany) #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Pure mathematics #Transversality #math.DG #math.SG #msc:32G20 #msc:53D18
paper · pdf · doi:10.1016/j.difgeo.2014.08.001
published as Differential Geom. Appl. 36 (2014), pp. 98-133 · 38 pages
arxiv created 2012/05/01 · openalex publication_date 2014/08/28 · arxiv updated 2014/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A generalized complex manifold which satisfies the ∂ ∂-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.