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  • Book
  • © 1988

Determinantal Rings

Authors:

  1. Winfried Bruns
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    You can also search for this author in PubMed   Google Scholar

  2. Udo Vetter
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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1327)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-vii
    PDF

  2. Preliminaries

    • Winfried Bruns, Udo Vetter
    Pages 1-9

  3. Ideals of maximal minors

    • Winfried Bruns, Udo Vetter
    Pages 10-26

  4. Generically perfect ideals

    • Winfried Bruns, Udo Vetter
    Pages 27-37

  5. Algebras with straightening law on posets of minors

    • Winfried Bruns, Udo Vetter
    Pages 38-49

  6. The structure of an ASL

    • Winfried Bruns, Udo Vetter
    Pages 50-63

  7. Integrity and normality. The singular locus

    • Winfried Bruns, Udo Vetter
    Pages 64-72

  8. Generic points and invariant theory

    • Winfried Bruns, Udo Vetter
    Pages 73-92

  9. The divisor class group and the canonical class

    • Winfried Bruns, Udo Vetter
    Pages 93-104

  10. Powers of ideals of maximal minors

    • Winfried Bruns, Udo Vetter
    Pages 105-121

  11. Primary decomposition

    • Winfried Bruns, Udo Vetter
    Pages 122-134

  12. Representation theory

    • Winfried Bruns, Udo Vetter
    Pages 135-152

  13. Principal radical systems

    • Winfried Bruns, Udo Vetter
    Pages 153-161

  14. Generic modules

    • Winfried Bruns, Udo Vetter
    Pages 162-173

  15. The module of Kähler differentials

    • Winfried Bruns, Udo Vetter
    Pages 174-183

  16. Derivations and rigidity

    • Winfried Bruns, Udo Vetter
    Pages 184-201

  17. Appendix

    • Winfried Bruns, Udo Vetter
    Pages 202-218

  18. Back Matter

    Pages 219-238
    PDF
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About this book

Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. Their study has attracted many prominent researchers and has motivated the creation of theories which may now be considered part of general commutative ring theory. The book gives a first coherent treatment of the structure of determinantal rings. The main approach is via the theory of algebras with straightening law. This approach suggest (and is simplified by) the simultaneous treatment of the Schubert subvarieties of Grassmannian. Other methods have not been neglected, however. Principal radical systems are discussed in detail, and one section is devoted to each of invariant and representation theory. While the book is primarily a research monograph, it serves also as a reference source and the reader requires only the basics of commutative algebra together with some supplementary material found in the appendix. The text may be useful for seminars following a course in commutative ring theory since a vast number of notions, results, and techniques can be illustrated significantly by applying them to determinantal rings.
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Keywords

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Bibliographic Information

  • Book Title: Determinantal Rings

  • Authors: Winfried Bruns, Udo Vetter

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0080378

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-19468-2Published: 22 June 1988

  • eBook ISBN: 978-3-540-39274-3Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 240

  • Topics: Group Theory and Generalizations, Topological Groups, Lie Groups

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Buy it now

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
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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