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Developments in Mathematics

The Grassmannian Variety

Geometric and Representation-Theoretic Aspects

Authors: Lakshmibai, V., Brown, Justin

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  • Presents an exciting playing field for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry
  • Comprehensive treatment brings graduate students and new researchers to the forefront of the field
  • Serves as excellent supplementary material for a graduate course on Grassmannian varieties
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eBook $69.99
price for USA in USD (gross)
  • ISBN 978-1-4939-3082-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.99
price for USA in USD
  • ISBN 978-1-4939-3081-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA in USD
  • ISBN 978-1-4939-5608-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this text uniquely presents an exciting playing field for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen–Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory.

This text would serve well as a reference book for a graduate work on Grassmannian varieties and would be an excellent supplementary text for several courses including those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric and differential topology, representation theory of compact and reductive groups, Lie theory, toric varieties, geometric representation theory, and singularity theory. The reader should have some familiarity with commutative algebra and algebraic geometry.

Reviews

“The present book gives a detailed treatment of the standard monomial theory (SMT) for the Grassmannians and their Schubert subvarieties along with several applications of SMT. It can be used as a reference book by experts and graduate students who study varieties with a reductive group action such as flag and toric varieties.” (Valentina Kiritchenko, zbMATH 1343.14001, 2016)

“The book under review is more elementary; it is exclusively devoted to Grassmannians and their Schubert subvarieties. The book is divided into three parts. … This is a nicely written book, one that may appeal to students and researchers in related areas.” (Felipe Zaldivar, MAA Reviews, maa.org, December, 2015)


Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-1-4939-3082-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.99
price for USA in USD
  • ISBN 978-1-4939-3081-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA in USD
  • ISBN 978-1-4939-5608-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Grassmannian Variety
Book Subtitle
Geometric and Representation-Theoretic Aspects
Authors
Series Title
Developments in Mathematics
Series Volume
42
Copyright
2015
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4939-3082-1
DOI
10.1007/978-1-4939-3082-1
Hardcover ISBN
978-1-4939-3081-4
Softcover ISBN
978-1-4939-5608-1
Series ISSN
1389-2177
Edition Number
1
Number of Pages
X, 172
Number of Illustrations
84 b/w illustrations, 39 illustrations in colour
Topics