Lecture Notes in Mathematics

The Lefschetz Properties

Authors: Harima, T., Maeno, T., Morita, H., Numata, Y., Wachi, A., Watanabe, J.

  • This is the first book on the theory of Lefschetz properties
  • This is the first attempt to treat the theory of Lefschetz properties systematically
  • This book shows a wide connection of the Lefschetz properties to other areas of mathematics
  • So, Researchers from various area of mathematics should be interested in this book
  • This book contains many open problems
  • Some new results are contained (Some of them may appear as papers elsewhere. Some of them may not.)
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eBook $44.99
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  • ISBN 978-3-642-38206-2
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Softcover $59.99
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  • ISBN 978-3-642-38205-5
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About this book

This is a monograph which collects basic techniques, major results and interesting applications of Lefschetz properties of Artinian algebras. The origin of the Lefschetz properties of Artinian algebras is the Hard Lefschetz Theorem, which is a major result in algebraic geometry. However, for the last two decades, numerous applications of the Lefschetz properties to other areas of mathematics have been found, as a result of which the theory of the Lefschetz properties is now of great interest in its own right. It also has ties to other areas, including combinatorics, algebraic geometry, algebraic topology, commutative algebra and representation theory. The connections between the Lefschetz property and other areas of mathematics are not only diverse, but sometimes quite surprising, e.g. its ties to the Schur-Weyl duality. This is the first book solely devoted to the Lefschetz properties and is the first attempt to treat those properties systematically.

Table of contents (9 chapters)

  • Poset Theory

    Harima, Tadahito (et al.)

    Pages 1-38

  • Basics on the Theory of Local Rings

    Harima, Tadahito (et al.)

    Pages 39-95

  • Lefschetz Properties

    Harima, Tadahito (et al.)

    Pages 97-140

  • Complete Intersections with the SLP

    Harima, Tadahito (et al.)

    Pages 141-156

  • A Generalization of Lefschetz Elements

    Harima, Tadahito (et al.)

    Pages 157-170

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-38206-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA
  • ISBN 978-3-642-38205-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Lefschetz Properties
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2080
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-38206-2
DOI
10.1007/978-3-642-38206-2
Softcover ISBN
978-3-642-38205-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIX, 250
Number of Illustrations and Tables
20 b/w illustrations
Topics