LEADER 04420nam 22006615 450 001 9910300241803321 005 20221012213058.0 010 $a1-4939-3082-6 024 7 $a10.1007/978-1-4939-3082-1 035 $a(CKB)3710000000478732 035 $a(EBL)4178118 035 $a(SSID)ssj0001585159 035 $a(PQKBManifestationID)16264055 035 $a(PQKBTitleCode)TC0001585159 035 $a(PQKBWorkID)14864897 035 $a(PQKB)10253464 035 $a(DE-He213)978-1-4939-3082-1 035 $a(MiAaPQ)EBC4178118 035 $a(PPN)190530340 035 $a(EXLCZ)993710000000478732 100 $a20150925d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe Grassmannian variety $egeometric and representation-theoretic aspects /$fby V. Lakshmibai, Justin Brown 205 $a1st ed. 2015. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2015. 215 $a1 online resource (174 p.) 225 1 $aDevelopments in Mathematics,$x1389-2177 ;$v42 300 $aDescription based upon print version of record. 320 $aIncludes bibliographical references and index. 327 $aPreface -- 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. 330 $aThis book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this  text uniquely presents an exciting playing field  for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen?Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. This text would serve well as a reference book for a graduate work on Grassmannian varieties and would be an excellent supplementary text for several courses including those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric and differential topology, representation theory of compact and reductive groups, Lie theory, toric varieties, geometric representation theory, and singularity theory. The reader should have some familiarity with commutative algebra and algebraic geometry. 410 0$aDevelopments in Mathematics,$x1389-2177 ;$v42 606 $aGeometry, Algebraic 606 $aAlgebraic topology 606 $aCombinatorial analysis 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 615 0$aGeometry, Algebraic. 615 0$aAlgebraic topology. 615 0$aCombinatorial analysis. 615 14$aAlgebraic Geometry. 615 24$aAlgebraic Topology. 615 24$aCombinatorics. 676 $a512.2 700 $aLakshmibai$b V$4aut$4http://id.loc.gov/vocabulary/relators/aut$0955751 702 $aBrown$b Justin$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300241803321 996 $aThe Grassmannian Variety$92533257 997 $aUNINA