Homogeneous Spaces and Equivariant Embeddings

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1、HomogeneousspacesandequivariantembeddingsD.A.TimashevJanuary10,2006arXiv:math.AG/0602228v110Feb2006ContentsIntroduction31Algebraichomogeneousspaces81Homogeneousspaces.......................82Fibrations,bundles,andrepresentations............103Classesofhomogeneousspaces..

2、................182Complexityandrank224Localstructuretheorems.....................235ComplexityandrankofG-varieties...............276Complexityandmodality.....................317Horosphericalvarieties......................358Geometryofcotangentbundle..................389

3、Complexityandrankofhomogeneousspaces..........4710Spacesofsmallrankandcomplexity..............5111Doublecones...........................573Generaltheoryofembeddings6612TheLuna–Vusttheory......................6713B-charts..............................7214ClassificationofG-

4、models....................7615Caseofcomplexity0.......................7816Caseofcomplexity1.......................8317Divisors..............................9618Intersectiontheory........................1064Invariantvaluations11819G-valuations............................1

5、1920Valuationcones..........................12221Centralvaluations.........................12922LittleWeylgroup.........................1341CONTENTS223Invariantcollectivemotion....................14024Formalcurves...........................1485Sphericalvarieties15225Vari

6、ouscharacterizationsofsphericity..............15326Symmetricspaces.........................16427Algebraicmonoidsandgroupembeddings...........17928S-varieties.............................19129Toroidalembeddings.......................19730Wonderfulvarieties................

7、........20331Frobeniussplitting........................219Appendix226A1Rationalmodulesandlinearization...............226A2Invarianttheory..........................228A3Geometricvaluations.......................232A4Schematicpoints.........................234Bibliography2

8、36IntroductionGroupsenteredmathematicsastransformationgroups.FromtheworksofCaleyandKleinitbecameclearth