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Period Mappings with Applications to Symplectic Complex Spaces

  • Tim Kirschner

Part of the Lecture Notes in Mathematics book series (LNM, volume 2140)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Tim Kirschner
    Pages 143-212
  3. Back Matter
    Pages 213-278

About this book

Introduction

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.

Keywords

14F05,18F20,32C35,32C20,14D05,14D07,14J32,32Q25,18G40. Frölicher spectral sequence Gauß-Manin connection Period mapping Symplectic variety Torelli theorem

Authors and affiliations

  • Tim Kirschner
    • 1
  1. 1.Mathematisches InstitutUniversität BayreuthBayreuthGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-17521-8
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-17520-1
  • Online ISBN 978-3-319-17521-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site