Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

Mixed Hodge Structures

Authors: Peters, Christiaan, Steenbrink, Joseph H. M.

  • Comprehensive basic monograph on mixed Hodge structures
  • Explains Delingne's mixed Hodge theory in a detailed and exhaustive fashion
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About this book

The text of this book has its origins more than twenty- ve years ago. In the seminar of the Dutch Singularity Theory project in 1982 and 1983, the second-named author gave a series of lectures on Mixed Hodge Structures and Singularities, accompanied by a set of hand-written notes. The publication of these notes was prevented by a revolution in the subject due to Morihiko Saito: the introduction of the theory of Mixed Hodge Modules around 1985. Understanding this theory was at the same time of great importance and very hard, due to the fact that it uni es many di erent theories which are quite complicated themselves: algebraic D-modules and perverse sheaves. The present book intends to provide a comprehensive text about Mixed Hodge Theory with a view towards Mixed Hodge Modules. The approach to Hodge theory for singular spaces is due to Navarro and his collaborators, whose results provide stronger vanishing results than Deligne’s original theory. Navarro and Guill en also lled a gap in the proof that the weight ltration on the nearby cohomology is the right one. In that sense the present book corrects and completes the second-named author’s thesis.

Reviews

From the reviews:

"This book is dealing with Hodge Theory ... which generalizes in a functorial way the variations of MHS. ... The clarity of the presentation and the wealth of information are both remarkable. This book ... is a masterpiece that anyone working in Algebraic Geometry, Singularities or Analytic/Complex Geometry would like to have in his own library." (Alexandru Dimca, Zentralblatt MATH, Vol. 1138 (16), 2008)

"The book under review … focuses mainly on the ‘pure’ story just summarized, is aimed at graduate students and researchers … . The book begins with a brief historical survey; each chapter is headed by a good summary of its contents and concluded by historical remarks (with references). … this work is a thoroughly readable and very up-to-date account of mixed Hodge theory, written by masters of the subject, and will undoubtedly serve as a basic reference for years to come." (Matt Kerr, Mathematical Reviews, Issue 2009 C)

“This book has been awaited for many years. … the book which is now available will certainly rapidly become one of the standard references on the topic. Hodge theory assigns to a complex variety data which come from linear algebra. … I heartily recommend the book.” (Helene Esnault, Jahresbericht der Deutsche Mathematiker Vereinigung, Vol. 112 (1), 2010)

Table of contents (15 chapters)

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-3-540-77017-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-3-540-77015-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-3-642-09574-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Mixed Hodge Structures
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
52
Copyright
2008
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-77017-6
DOI
10.1007/978-3-540-77017-6
Hardcover ISBN
978-3-540-77015-2
Softcover ISBN
978-3-642-09574-0
Series ISSN
0071-1136
Edition Number
1
Number of Pages
XIV, 470
Number of Illustrations and Tables
6 b/w illustrations
Topics