ENGLISH

Period Mappings with Applications to Symplectic Complex Spaces

By Tim Kirschner (auth.)

Book information

Publisher
Springer International Publishing
Year
2015
ISBN
978-3-319-17520-1, 978-3-319-17521-8
DOI
10.1007/978-3-319-17521-8
Language
english
Format
PDF
Filesize
10 MB (10529170 bytes)
Series
Lecture Notes in Mathematics 2140
Edition
1
Pages
XVIII, 275\295
Time added
2015-11-25 16:51:03
Algebraic Geometry; Several Complex Variables andHomological Algebra

Description

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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