04420nam 22006615 450 991030024180332120221012213058.01-4939-3082-610.1007/978-1-4939-3082-1(CKB)3710000000478732(EBL)4178118(SSID)ssj0001585159(PQKBManifestationID)16264055(PQKBTitleCode)TC0001585159(PQKBWorkID)14864897(PQKB)10253464(DE-He213)978-1-4939-3082-1(MiAaPQ)EBC4178118(PPN)190530340(EXLCZ)99371000000047873220150925d2015 u| 0engur|n|---|||||txtccrThe Grassmannian variety geometric and representation-theoretic aspects /by V. Lakshmibai, Justin Brown1st ed. 2015.New York, NY :Springer New York :Imprint: Springer,2015.1 online resource (174 p.)Developments in Mathematics,1389-2177 ;42Description based upon print version of record.Includes bibliographical references and index.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.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.Developments in Mathematics,1389-2177 ;42Geometry, AlgebraicAlgebraic topologyCombinatorial analysisAlgebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Algebraic Topologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28019Combinatoricshttps://scigraph.springernature.com/ontologies/product-market-codes/M29010Geometry, Algebraic.Algebraic topology.Combinatorial analysis.Algebraic Geometry.Algebraic Topology.Combinatorics.512.2Lakshmibai Vauthttp://id.loc.gov/vocabulary/relators/aut955751Brown Justinauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910300241803321The Grassmannian Variety2533257UNINA00991nam0 22002651i 450 UON0001010320231205101929.67520020107d1950 |0itac50 baengGB|||| |||||ˆThe ‰Arabs in historyBernard LewisLondonMaurice Powicke Hutchinson's University Library Anchor Press1950196 p.19 cmArabiaStoria islamicaUONC002555FIGBLondonUONL003044ARA IVPAESI ARABI - STORIAALewisBernardUONV0022421207Hutchinson UniversityUONV248054650ITSOL20251114RICASIBA - SISTEMA BIBLIOTECARIO DI ATENEOUONSIUON00010103SIBA - SISTEMA BIBLIOTECARIO DI ATENEOSI ARA IV 137 SI MR 36899 5 137 Arabs in history28346UNIOR