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  • Book
  • © 2013

The Lefschetz Properties

Authors:

  1. Tadahito Harima

    1. Department of Mathematical Education, Niigata University, Nishi-Ku, Japan

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  2. Toshiaki Maeno

    1. Meijo University Department of Mathematics, Nagoya, Japan

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  3. Hideaki Morita

    1. Muroran Institute of Technology, Muroran, Japan

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  4. Yasuhide Numata

    1. Department of Mathematical Sciences, Shinshu University, Matsumoto, Japan

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  5. Akihito Wachi

    1. Hokkaido University of Education Department of Mathematics, Kushiro, Japan

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  6. Junzo Watanabe

    1. Tokai University Department of Mathematics, Hiratsuka, Japan

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  • 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.)
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2080)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xix
    PDF

  2. Poset Theory

    • Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 1-38

  3. Basics on the Theory of Local Rings

    • Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 39-95

  4. Lefschetz Properties

    • Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 97-140

  5. Complete Intersections with the SLP

    • Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 141-156

  6. A Generalization of Lefschetz Elements

    • Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 157-170

  7. k-Lefschetz Properties

    • Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 171-188

  8. Cohomology Rings and the Strong Lefschetz Property

    • Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 189-199

  9. Invariant Theory and Lefschetz Properties

    • Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 201-209

  10. The Strong Lefschetz Property and the Schur–Weyl Duality

    • Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 211-234

  11. Back Matter

    Pages 235-252
    PDF
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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.
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Keywords

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Authors and Affiliations

  • Department of Mathematical Education, Niigata University, Nishi-Ku, Japan

    Tadahito Harima

  • Meijo University Department of Mathematics, Nagoya, Japan

    Toshiaki Maeno

  • Muroran Institute of Technology, Muroran, Japan

    Hideaki Morita

  • Department of Mathematical Sciences, Shinshu University, Matsumoto, Japan

    Yasuhide Numata

  • Hokkaido University of Education Department of Mathematics, Kushiro, Japan

    Akihito Wachi

  • Tokai University Department of Mathematics, Hiratsuka, Japan

    Junzo Watanabe

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Bibliographic Information

  • Book Title: The Lefschetz Properties

  • Authors: Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-38206-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2013

  • Softcover ISBN: 978-3-642-38205-5Published: 30 August 2013

  • eBook ISBN: 978-3-642-38206-2Published: 23 August 2013

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIX, 250

  • Number of Illustrations: 20 b/w illustrations

  • Topics: Algebra, Algebraic Geometry, Combinatorics

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Buy it now

eBook USD 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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