Justin Brown: The Grassmannian Variety | Buch

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Cover: 9781493930814 | The Grassmannian Variety | Justin Brown (u. a.) | Buch | Englisch

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Sprache: 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.

Zusammenfassung

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

Comprehensive treatment brings graduate students and new researchers to the forefront of the field

Serves as excellent supplementary material for a graduate course on Grassmannian varieties

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2015
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	184
Reihe:	Developments in Mathematics
Inhalt:	x 172 S. 84 s/w Illustr. 39 farbige Illustr. 172 p. 123 illus. 39 illus. in color.
ISBN-13:	9781493930814
ISBN-10:	1493930818
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Brown, Justin Lakshmibai, V.
Auflage:	1st ed. 2015
Hersteller:	Springer US Springer New York Developments in Mathematics
Maße:	241 x 160 x 16 mm
Von/Mit:	Justin Brown (u. a.)
Erscheinungsdatum:	26.09.2015
Gewicht:	0,448 kg