國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

The Grassmannian varietygeometric an...

Brown, Justin.

The Grassmannian varietygeometric and representation-theoretic aspects /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The Grassmannian varietyby V. Lakshmibai, Justin Brown.
其他題名:	geometric and representation-theoretic aspects /
作者:	Lakshmibai, V.
其他作者:	Brown, Justin.
出版者:	New York, NY :Springer New York :2015.
面頁冊數:	x, 172 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Representations of groups.
電子資源:	http://dx.doi.org/10.1007/978-1-4939-3082-1
ISBN:	9781493930821$q(electronic bk.)

The Grassmannian varietygeometric and representation-theoretic aspects /
Lakshmibai, V.

The Grassmannian varietygeometric and representation-theoretic aspects /[electronic resource] :by V. Lakshmibai, Justin Brown. - New York, NY :Springer New York :2015. - x, 172 p. :ill., digital ;24 cm. - Developments in mathematics,v.421389-2177 ;. - Developments in mathematics ;v.25..

Preface -- 1. Introduction -- Part I. Algebraic Geometry -- A Brief Recollection - 2. Preliminary Material -- 3. Cohomology Theory -- 4. Grobner 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.

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.

ISBN: 9781493930821$q(electronic bk.)

Standard No.: 10.1007/978-1-4939-3082-1doiSubjects--Topical Terms:

191076
Representations of groups.

LC Class. No.: QA176

Dewey Class. No.: 512.22

The Grassmannian varietygeometric and representation-theoretic aspects /
LDR:03128nmm a2200325 a 4500 001 476894
003 DE-He213
005 20160412115211.0
006 m d
007 cr nn 008maaau
008 160526s2015 nyu s 0 eng d
020 $a 9781493930821$q(electronic bk.)
020 $a 9781493930814$q(paper)
024 7 $a 10.1007/978-1-4939-3082-1 $2 doi
035 $a 978-1-4939-3082-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA176
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
082 0 4 $a 512.22 $2 23
090 $a QA176 $b .L192 2015
100 1 $a Lakshmibai, V. $3 731677
245 1 4 $a The Grassmannian variety $h [electronic resource] : $b geometric and representation-theoretic aspects / $c by V. Lakshmibai, Justin Brown.
260 $a New York, NY : $b Springer New York : $b Imprint: Springer, $c 2015.
300 $a x, 172 p. : $b ill., digital ; $c 24 cm.
490 1 $a Developments in mathematics, $x 1389-2177 ; $v v.42
505 0 $a Preface -- 1. Introduction -- Part I. Algebraic Geometry -- A Brief Recollection - 2. Preliminary Material -- 3. Cohomology Theory -- 4. Grobner 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.
520 $a 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.
650 0 $a Representations of groups. $3 191076
650 0 $a Geometry. $3 183883
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Algebraic Geometry. $3 274807
650 2 4 $a Algebraic Topology. $3 273784
650 2 4 $a Combinatorics. $3 274788
700 1 $a Brown, Justin. $3 731678
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Developments in mathematics ; $v v.25. $3 558834
856 4 0 $u http://dx.doi.org/10.1007/978-1-4939-3082-1
950 $a Mathematics and Statistics (Springer-11649)