The Grassmannian Variety: Geometric and Representation-Theoretic Aspects
暫譯: 格拉斯曼流形:幾何與表示理論的面向
Lakshmibai, V., Brown, Justin
- 出版商: Springer
- 出版日期: 2015-09-26
- 售價: $3,640
- 貴賓價: 9.5 折 $3,458
- 語言: 英文
- 頁數: 172
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 1493930818
- ISBN-13: 9781493930814
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相關分類:
物理學 Physics
海外代購書籍(需單獨結帳)
商品描述
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.
商品描述(中文翻譯)
這本書全面探討了Grassmannian變數及其Schubert子變數,重點關注Grassmannian變數的幾何和表示理論方面。Grassmannian變數的研究位於交換代數、代數幾何、表示理論和組合學的交叉點。因此,本書為數學、物理和計算機科學的研究生和研究人員提供了一個獨特而令人興奮的舞台,以擴展他們在代數幾何領域的知識。書中介紹了Grassmannian變數及其Schubert子變數的標準單項式理論(SMT),並展示了一些SMT的重要應用,包括Cohen-Macaulay性質、正規性、唯一因子性、Gorenstein性質、Schubert變數的奇異位置、Schubert變數的錐退化,以及Schubert變數與經典不變理論之間的關係。
本書將作為研究Grassmannian變數的研究生參考書籍,並且是幾門課程的優秀補充教材,包括球面變數的幾何、Schubert變數、高級幾何和微分拓撲主題、緊緻和還原群的表示理論、李理論、錐變數、幾何表示理論和奇異性理論。讀者應對交換代數和代數幾何有一定的熟悉度。