Variation of Hodge Structure for Generalized Complex Manifolds

          @misc{ scivideos_PIRSA:12050023,
            doi = {10.48660/12050023},
            url = {https://pirsa.org/12050023},
            author = {Baraglia, David},
            keywords = {},
            language = {en},
            title = {Variation of Hodge Structure for Generalized Complex Manifolds},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2012},
            month = {may},
            note = {PIRSA:12050023 see, \url{https://scivideos.org/index.php/pirsa/12050023}}
          }
          

Abstract

Generalized complex manifolds, like complex manifolds, admit a decomposition of the bundle of di
erential forms. When an analogue of the @ @ lemma holds there is a corresponding Hodge decomposition in twisted cohomology. We look at some aspects of this decomposition, in particular its behavior under deformations of generalized complex structure. We de ne period maps and show a Griths transversality result. We use Courant algebroids to develop the notion of a holomorphic family of generalized complex structures and show the period maps for such families are holomorphic.