000 02984nam a22004575i 4500
001 978-3-642-18399-7
003 DE-He213
005 20140220083754.0
007 cr nn 008mamaa
008 110406s2011 gw | s |||| 0|eng d
020 _a9783642183997
_9978-3-642-18399-7
024 7 _a10.1007/978-3-642-18399-7
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
082 0 4 _a516.35
_223
100 1 _aTimashev, D.A.
_eauthor.
245 1 0 _aHomogeneous Spaces and Equivariant Embeddings
_h[electronic resource] /
_cby D.A. Timashev.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2011.
300 _aXXII, 254 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aEncyclopaedia of Mathematical Sciences,
_x0938-0396 ;
_v138
505 0 _aIntroduction.- 1 Algebraic Homogeneous Spaces -- 2 Complexity and Rank -- 3 General Theory of Embeddings -- 4 Invariant Valuations -- 5 Spherical Varieties -- Appendices -- Bibliography -- Indices.
520 _aHomogeneous spaces of linear algebraic groups lie at the crossroads of algebraic geometry, theory of algebraic groups, classical projective and enumerative geometry, harmonic analysis, and representation theory. By standard reasons of algebraic geometry, in order to solve various problems on a homogeneous space, it is natural and helpful to compactify it while keeping track of the group action, i.e., to consider equivariant completions or, more generally, open embeddings of a given homogeneous space. Such equivariant embeddings are the subject of this book. We focus on the classification of equivariant embeddings in terms of certain data of "combinatorial" nature (the Luna-Vust theory) and description of various geometric and representation-theoretic properties of these varieties based on these data. The class of spherical varieties, intensively studied during the last three decades, is of special interest in the scope of this book. Spherical varieties include many classical examples, such as Grassmannians, flag varieties, and varieties of quadrics, as well as well-known toric varieties. We have attempted to cover most of the important issues, including the recent substantial progress obtained in and around the theory of spherical varieties.
650 0 _aMathematics.
650 0 _aGeometry, algebraic.
650 0 _aTopological Groups.
650 1 4 _aMathematics.
650 2 4 _aAlgebraic Geometry.
650 2 4 _aTopological Groups, Lie Groups.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642183980
830 0 _aEncyclopaedia of Mathematical Sciences,
_x0938-0396 ;
_v138
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-18399-7
912 _aZDB-2-SMA
999 _c107435
_d107435