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The Resource The Grassmannian Variety : Geometric and RepresentationTheoretic Aspects, by V. Lakshmibai, Justin Brown, (electronic resource)
The Grassmannian Variety : Geometric and RepresentationTheoretic Aspects, by V. Lakshmibai, Justin Brown, (electronic resource)
Resource Information
The item The Grassmannian Variety : Geometric and RepresentationTheoretic Aspects, by V. Lakshmibai, Justin Brown, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item The Grassmannian Variety : Geometric and RepresentationTheoretic Aspects, by V. Lakshmibai, Justin Brown, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representationtheoretic 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
 Language
 eng
 Edition
 1st ed. 2015.
 Extent
 X, 172 p. 123 illus., 39 illus. in color.
 Contents

 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 RepresentationTheoretic Aspects
 9. Relationship to Classical Invariant Theory
 10. Determinantal Varieties
 11. Related Topics
 References
 List of Symbols
 Index
 Isbn
 9781493930821
 Label
 The Grassmannian Variety : Geometric and RepresentationTheoretic Aspects
 Title
 The Grassmannian Variety
 Title remainder
 Geometric and RepresentationTheoretic Aspects
 Statement of responsibility
 by V. Lakshmibai, Justin Brown
 Subject

 Algebraic Topology
 Algebraic geometry
 Algebraic geometry
 Algebraic geometry
 Algebraic topology
 Algebraic topology
 Algebraic topology
 Combinatorics
 Combinatorics
 Combinatorics
 Electronic resources
 Mathematics
 Mathematics
 Mathematics
 Algebraic Geometry
 Algebraic Geometry
 Algebraic Geometry
 Algebraic Topology
 Algebraic Topology
 Language
 eng
 Summary
 This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representationtheoretic 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
 http://library.link/vocab/creatorName
 Lakshmibai, V
 Image bit depth
 0
 LC call number
 QA564609
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName

 Brown, Justin.
 SpringerLink
 Series statement
 Developments in Mathematics,
 Series volume
 42
 http://library.link/vocab/subjectName

 Mathematics
 Algebraic geometry
 Algebraic topology
 Combinatorics
 Mathematics
 Algebraic Geometry
 Algebraic Topology
 Combinatorics
 Label
 The Grassmannian Variety : Geometric and RepresentationTheoretic Aspects, by V. Lakshmibai, Justin Brown, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 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 RepresentationTheoretic Aspects  9. Relationship to Classical Invariant Theory  10. Determinantal Varieties  11. Related Topics  References  List of Symbols  Index
 Dimensions
 unknown
 Edition
 1st ed. 2015.
 Extent
 X, 172 p. 123 illus., 39 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9781493930821
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9781493930821
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9781493930821
 Label
 The Grassmannian Variety : Geometric and RepresentationTheoretic Aspects, by V. Lakshmibai, Justin Brown, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 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 RepresentationTheoretic Aspects  9. Relationship to Classical Invariant Theory  10. Determinantal Varieties  11. Related Topics  References  List of Symbols  Index
 Dimensions
 unknown
 Edition
 1st ed. 2015.
 Extent
 X, 172 p. 123 illus., 39 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9781493930821
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9781493930821
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9781493930821
Subject
 Algebraic Topology
 Algebraic geometry
 Algebraic geometry
 Algebraic geometry
 Algebraic topology
 Algebraic topology
 Algebraic topology
 Combinatorics
 Combinatorics
 Combinatorics
 Electronic resources
 Mathematics
 Mathematics
 Mathematics
 Algebraic Geometry
 Algebraic Geometry
 Algebraic Geometry
 Algebraic Topology
 Algebraic Topology
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