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The Grassmannian Variety
V. Lakshmibai, Justin Brown (Broschiert, Englisch)
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Beschreibung
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. 96,29 €
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Technische Daten
Erscheinungsdatum
29.10.2016
Sprache
Englisch
EAN
9781493956081
Herausgeber
Springer US
Serien- oder Bandtitel
Developments in Mathematics
Sonderedition
Nein
Autor
V. Lakshmibai, Justin Brown
Seitenanzahl
172
Einbandart
Broschiert
Buch Untertitel
Geometric and Representation-Theoretic Aspects
Schlagwörter
Bott-Samelson varieties, Cohen-Macaulay property, Flag varieties, Geometry of spherical varieties, Gorenstein property, Groebner bases, Schubert varieties, Singular locus, Standard monomial theory, The Grassmannian variety, algebraic geometry, classical invariant theory, combinatorics
Thema-Inhalt
PBMW - Algebraische Geometrie
PBPD - Algebraische Topologie
PBD - Diskrete Mathematik
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Humana, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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