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Lecture Notes in Mathematics

Period Mappings with Applications to Symplectic Complex Spaces

Authors: Kirschner, Tim

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  • Presents sheaves with a clear connection to the set-theoretic foundations
  • Strives for a maximum of rigor (concerning proofs, statements, definitions, and notation)
  • Overcomes the “canonical isomorphism” paradigm; all morphisms are given/constructed explicitly
  • Introduces a Gauß-Manin connection for families of possibly non-compact manifolds
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eBook 41,64 €
price for Spain (gross)
  • ISBN 978-3-319-17521-8
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Softcover 51,99 €
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  • ISBN 978-3-319-17520-1
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About this book

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.

Reviews

“The book under review aims to extend a number of methods and results from algebraic geometry (schemes and algebraic varieties) to the theory of complex analytic spaces. … The book is very clearly written, with almost all prerequisites collected in two appendices. In this way it is interesting not only for the original results it contains, but also as an introduction to this area lying at the intersection of algebraic and complex geometry.” (Andrei D. Halanay, Mathematical Reviews, December, 2016) 


Table of contents (3 chapters)

Table of contents (3 chapters)

Buy this book

eBook 41,64 €
price for Spain (gross)
  • ISBN 978-3-319-17521-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-319-17520-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Period Mappings with Applications to Symplectic Complex Spaces
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2140
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-17521-8
DOI
10.1007/978-3-319-17521-8
Softcover ISBN
978-3-319-17520-1
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVIII, 275
Topics