TY  - GEN
AU  - Kirschner,Tim
TI  - Period mappings with applications to symplectic complex spaces
T2  - Lecture notes in mathematics
SN  - 9783319175201
U1  - 516.35 23
PY  - 2015///
CY  - Switzerland
PB  - Springer
KW  - Algebraic geometry.
KW  - Complex numbers.
KW  - Symplectic spaces.
N1  - 1. Period mappings for families of complex manifolds --
2. Degeneration of the Frolicher spectral sequence --
3. Symplectic complex spaces --
A. Foundations and conventions --
B. Tools --
Terminology
N2  - 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
ER  -