Overview
- Excellent overview of the theory of Schubert varieties
- Includes supplementary material: sn.pub/extras
Part of the book series: Encyclopaedia of Mathematical Sciences (EMS, volume 137)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Schubert varieties lie at the cross roads of algebraic geometry, combinatorics, commutative algebra, and representation theory. They are an important class of subvarieties of flag varieties, interesting in their own right, and providing an inductive tool for studying flag varieties. The literature on them is vast, for they are ubiquitous - they have been intensively studied over the last fifty years, from many different points of view.
This book is mainly a detailed account of a particularly interesting instance of their occurrence: namely, in relation to classical invariant theory. More precisely, it is about the connection between the first and second fundamental theorems of classical invariant theory and standard monomial theory for Schubert varieties in certain special flag varieties. Historically, this connection was the prime motivation for the development of standard monomial theory. Determinantal varieties and basic concepts of geometric invariant theory arise naturally in establishing the connection.
Reviews
From the reviews:
"The goal of the book is to present the results of Classical Invariant Theory (CIT) and Standard Monomial Theory (SMT) and the connection between the two theories. … The book is written for a broad audience including prospective graduate students and young researchers. The exposition is self-contained. It may be used for a year long course on Invariant Theory and Schubert varieties." (Dmitrii A. Timashëv, Mathematical Reviews, Issue 2008 m)
"The book aims to describe the beautiful connection between Schubert varieties and their Standard Monomial Theory (SMT) on the one hand and Classical Invariant Theory (CIT) on the other. … make the presentation self-contained keeping in mind the needs of prospective graduate students and young researchers. … The book may be recommended as a nice introduction to SMT and related active research areas. It may be used for a year long course on Invariant Theory and Schubert varieties." (Ivan V. Arzhantsev, Zentralblatt MATH, Vol. 1137 (15), 2008)
Authors and Affiliations
Bibliographic Information
Book Title: Standard Monomial Theory
Book Subtitle: Invariant Theoretic Approach
Authors: Venkatramani Lakshmibai, Komaranapuram N. Raghavan
Series Title: Encyclopaedia of Mathematical Sciences
DOI: https://doi.org/10.1007/978-3-540-76757-2
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2008
Hardcover ISBN: 978-3-540-76756-5Published: 29 January 2008
Softcover ISBN: 978-3-642-09543-6Published: 22 November 2010
eBook ISBN: 978-3-540-76757-2Published: 23 December 2007
Series ISSN: 0938-0396
Edition Number: 1
Number of Pages: XIV, 266
Topics: Algebraic Geometry, Algebra