Period mappings with applications to symplectic complex spaces (Q2343001)

The theme of this book is to extend Griffiths' classical theory of period mappings for compact Kähler manifolds to families of complex manifolds that are neither compact nor of Kähler type. The first chapter of the book is devoted to defining a more general notion of period mappings under the framework of a composable pair of maps and a right exact triple in the category of complex spaces. The second chapter studies the degeneration behavior of the relative Frolicher spectral sequence associated to a submersive morphism of complex manifolds. The last chapter applies chapter 1 and 2 to the study of (possibly singular) symplectic complex spaces which generalizes the notion of holomorphic symplectic manifolds, and proves a local Torelli theorem and a so-called Fujiki relation for such spaces.