Coverart for item
The Resource The Grassmannian Variety : Geometric and Representation-Theoretic Aspects, by V. Lakshmibai, Justin Brown, (electronic resource)

The Grassmannian Variety : Geometric and Representation-Theoretic Aspects, by V. Lakshmibai, Justin Brown, (electronic resource)

Label
The Grassmannian Variety : Geometric and Representation-Theoretic Aspects
Title
The Grassmannian Variety
Title remainder
Geometric and Representation-Theoretic Aspects
Statement of responsibility
by V. Lakshmibai, Justin Brown
Creator
Contributor
Author
Subject
Language
eng
Summary
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
Member of
http://library.link/vocab/creatorName
Lakshmibai, V
Image bit depth
0
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Brown, Justin.
  • SpringerLink (Online service)
Series statement
Developments in Mathematics,
Series volume
42
http://library.link/vocab/subjectName
  • Mathematics
  • Algebraic geometry
  • Algebraic topology
  • Combinatorics
Label
The Grassmannian Variety : Geometric and Representation-Theoretic Aspects, by V. Lakshmibai, Justin Brown, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-1-4939-3082-1
Instantiates
Publication
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 Representation-Theoretic Aspects -- 9. Relationship to Classical Invariant Theory -- 10. Determinantal Varieties -- 11. Related Topics -- References -- List of Symbols -- Index
Control code
978-1-4939-3082-1
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
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9781493930821
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-1-4939-3082-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086474096
Label
The Grassmannian Variety : Geometric and Representation-Theoretic Aspects, by V. Lakshmibai, Justin Brown, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-1-4939-3082-1
Publication
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 Representation-Theoretic Aspects -- 9. Relationship to Classical Invariant Theory -- 10. Determinantal Varieties -- 11. Related Topics -- References -- List of Symbols -- Index
Control code
978-1-4939-3082-1
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
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9781493930821
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-1-4939-3082-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086474096

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