Period Mappings with Applications to Symplectic Complex Spaces: 2140 (Lecture Notes in Mathematics, 2140) - Softcover

Kirschner, Tim

Softcover

ISBN 10: 3319175203 ISBN 13: 9783319175201

Publisher: Springer, 2015

Synopsis

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.

About this title

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2015
• Language: English
• ISBN 10: 3319175203
• ISBN 13: 9783319175201
• Binding: Paperback
• Edition number: 1
• Number of pages: 293