EAN: 9783319175201

PERIOD MAPPINGS WITH APPLICATIONS TO SYMPLECTIC...

Extending Griffiths' classical theory of period mappings for compact Kähler manifolds  this
book develops and applies a theory of period mappings of Hodge-de Rham type for families of
open complex manifolds. The text consists of three parts. The first part develops the theory.
The second part investigates the degeneration behavior of the relative Frölicher spectral
sequence associated to a submersive morphism of complex manifolds. The third part applies the
preceding material to the study of irreducible symplectic complex spaces. The latter notion
generalizes the idea of an irreducible symplectic manifold  dubbed an irreducible hyperkähler
manifold in differential geometry  to possibly singular spaces. The three parts of the work are
of independent interest  but intertwine nicely.

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