Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2140)
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Table of contents (3 chapters)
Keywords
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.
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Bibliographic Information
Book Title: Period Mappings with Applications to Symplectic Complex Spaces
Authors: Tim Kirschner
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-17521-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Softcover ISBN: 978-3-319-17520-1Published: 25 September 2015
eBook ISBN: 978-3-319-17521-8Published: 15 September 2015
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XVIII, 275
Topics: Algebraic Geometry, Several Complex Variables and Analytic Spaces, Category Theory, Homological Algebra