Homogeneous Spaces and Equivariant Embeddings [recurso electrónico] / by D.A. Timashev.
Tipo de material: TextoSeries Encyclopaedia of Mathematical Sciences ; 138Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011Descripción: XXII, 254 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783642183997Tema(s): Mathematics | Geometry, algebraic | Topological Groups | Mathematics | Algebraic Geometry | Topological Groups, Lie GroupsFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 516.35 Clasificación LoC:QA564-609Recursos en línea: Libro electrónicoTipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
---|---|---|---|---|---|---|---|
Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA564 -609 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 375730-2001 |
Navegando Biblioteca Electrónica Estantes, Código de colección: Colección de Libros Electrónicos Cerrar el navegador de estanterías (Oculta el navegador de estanterías)
QA564 -609 Algebraic Surfaces | QA564 -609 Intersection Spaces, Spatial Homology Truncation, and String Theory | QA564 -609 Computational Approach to Riemann Surfaces | QA564 -609 Homogeneous Spaces and Equivariant Embeddings | QA564 -609 Complex and Differential Geometry | QA564 -609 Pseudo-periodic Maps and Degeneration of Riemann Surfaces | QA611 -614.97 Hyperbolic Manifolds and Discrete Groups |
Introduction.- 1 Algebraic Homogeneous Spaces -- 2 Complexity and Rank -- 3 General Theory of Embeddings -- 4 Invariant Valuations -- 5 Spherical Varieties -- Appendices -- Bibliography -- Indices.
Homogeneous 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.
19