Universitext

Geometric Invariant Theory

Over the Real and Complex Numbers

Authors: Wallach, Nolan R.

  • ​Designed for non-mathematicians, physics students as well for example,  who want to learn about this important area of mathematics
  • Well organized and touches upon the main subjects, which offer a deeper understanding of the orbit structure of an algebraic group
  • Painless presentation places the subject within reasonable reach for mathematics and physics student at the graduate level
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eBook $54.99
price for USA (gross)
  • ISBN 978-3-319-65907-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-319-65905-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

Geometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. This sophisticated topic is elegantly presented with enough background theory included to make the text accessible to advanced graduate students in mathematics and physics with diverse backgrounds in algebraic and differential geometry.  Throughout the book, examples are emphasized. Exercises add to the reader’s understanding of the material; most are enhanced with hints.

The exposition is divided into two parts. The first part, ‘Background Theory’, is organized as a reference for the rest of the book. It contains two chapters developing material in complex and real algebraic geometry and algebraic groups that are difficult to find in the literature. Chapter 1 emphasizes the relationship between the Zariski topology and the canonical Hausdorff topology of an algebraic variety over the complex numbers. Chapter 2 develops the interaction between Lie groups and algebraic groups. Part 2, ‘Geometric Invariant Theory’ consists of three chapters (3–5). Chapter 3 centers on the Hilbert–Mumford theorem and contains a complete development of the Kempf–Ness theorem and Vindberg’s theory. Chapter 4 studies the orbit structure of a reductive algebraic group on a projective variety emphasizing Kostant’s theory. The final chapter studies the extension of classical invariant theory to products of classical groups emphasizing recent applications of the theory to physics.

About the authors

Nolan R. Wallach is professor of mathematics at the University of California, San Diego. Awards include the Alfred Sloan Fellowship 1972-1974, the Linback Award for Research Excellence, 1977, Honorary Professor, University of Cordoba, Argentina, 1989, and Elected Fellow of the American Academy of Arts and Sciences, 2004. Professor Wallach has over 135 publications including (with Roe Goodman) Symmetry, Representations, and Invariants (Graduate Texts in Mathematics, vol. 255).

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Table of contents (5 chapters)

  • Algebraic Geometry

    Wallach, Nolan R.

    Pages 3-29

  • Lie Groups and Algebraic Groups

    Wallach, Nolan R.

    Pages 31-47

  • The Affine Theory

    Wallach, Nolan R.

    Pages 51-128

  • Weight Theory in Geometric Invariant Theory

    Wallach, Nolan R.

    Pages 129-153

  • Classical and Geometric Invariant Theory for Products of Classical Groups

    Wallach, Nolan R.

    Pages 155-186

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-319-65907-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-319-65905-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Invariant Theory
Book Subtitle
Over the Real and Complex Numbers
Authors
Series Title
Universitext
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Nolan R. Wallach
eBook ISBN
978-3-319-65907-7
DOI
10.1007/978-3-319-65907-7
Softcover ISBN
978-3-319-65905-3
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XIV, 190
Topics