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＜電子ブック＞
The Grassmannian Variety : Geometric and Representation-Theoretic Aspects / by V. Lakshmibai, Justin Brown
(Developments in Mathematics. ISSN:2197795X ; 42)

版	1st ed. 2015.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2015
本文言語	英語
大きさ	X, 172 p. 123 illus., 39 illus. in color : online resource
著者標目	*Lakshmibai, V author Brown, Justin author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Algebraic topology LCSH:Discrete mathematics FREE:Algebraic Geometry FREE:Algebraic Topology FREE:Discrete Mathematics
一般注記	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 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 textwould 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 HTTP:URL=https://doi.org/10.1007/978-1-4939-3082-1

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