The Grassmannian Variety Geometric and Representation-Theoretic Aspects /

• Main Authors: Lakshmibai, V. (Author), Brown, Justin (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2015.
• Edition: 1st ed. 2015.
• Series: Developments in Mathematics, 42
• Subjects: Mathematics.; Algebraic geometry.; Algebraic topology.; Combinatorics.; Algebraic Geometry.; Algebraic Topology.

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 geomet...

Table of Contents:

• Preface
• 1. Introduction
• Part I. Algebraic Geometry—A Brief Recollection - 2. Preliminary Material
• 3. Cohomology Theory
• 4. Gröbner Bases
• Part II. Grassmannian and Schubert Varieties
• 5. The Grassmannian and Its Schubert Varieties
• 6. Further Geometric Properties of Schubert Varieties
• 7. Flat Degenerations
• Part III. Flag Varieties and Related Varieties
• 8. The Flag Variety: Geometric and Representation-Theoretic Aspects
• 9. Relationship to Classical Invariant Theory
• 10. Determinantal Varieties
• 11. Related Topics
• References
• List of Symbols
• Index.