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The Grassmannian Variety = Geometric and Representation-Theoretic Aspects /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
The Grassmannian Variety/ by V. Lakshmibai, Justin Brown.
其他題名:
Geometric and Representation-Theoretic Aspects /
作者:
Lakshmibai, V.
其他作者:
Brown, Justin.
面頁冊數:
X, 172 p. 123 illus., 39 illus. in color.online resource. :
Contained By:
Springer Nature eBook
標題:
Algebraic geometry. -
電子資源:
https://doi.org/10.1007/978-1-4939-3082-1
ISBN:
9781493930821
The Grassmannian Variety = Geometric and Representation-Theoretic Aspects /
Lakshmibai, V.
The Grassmannian Variety
Geometric and Representation-Theoretic Aspects /[electronic resource] :by V. Lakshmibai, Justin Brown. - 1st ed. 2015. - X, 172 p. 123 illus., 39 illus. in color.online resource. - Developments in Mathematics,421389-2177 ;. - Developments in Mathematics,41.
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 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.
ISBN: 9781493930821
Standard No.: 10.1007/978-1-4939-3082-1doiSubjects--Topical Terms:
1255324
Algebraic geometry.
LC Class. No.: QA564-609
Dewey Class. No.: 516.35
The Grassmannian Variety = Geometric and Representation-Theoretic Aspects /
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