Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0728.14041
Vust, Thierry
Plongements d'espaces symétriques algébriques: Une classification. (Embeddings of algebraic symmetric spaces: a classification). (French)
[J] Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 17, No.2, 165-195 (1990). ISSN 0391-173X

Let G be a connected reductive algebraic group over an algebraically closed field of characteristic zero and let H be a subgroup of G. The homogeneous space G/H is called symmetric if there exists an involutive automorphism $\sigma$ of G such that $G\sp{\sigma}\subset H\subset N\sb G(G\sp{\sigma})$. An embedding of G/H means an equivariant open embedding G/H$\hookrightarrow X$ such that X is a normal integral algebraic G- variety. The main propositions in this paper describe the set ${}\sp P{\cal D}(G/H)$ of irreducible subvarieties of codimension 1 in G/H stable under P where P is a parabolic subgroup of G associated with $\sigma$, and the set ${\cal V}(G/H)$ of normalized discrete valuations of k(G/H) which is invariant with respect to G. It is known that there is a bijection $X\mapsto ({\cal D}\sb X,{\cal V}\sb X)$ between the set of simple embeddings of G/H and the set of admissible pairs where ${\cal D}\sb X\subseteq\sp P{\cal D}$, ${\cal V}\sb X\subseteq {\cal V}(G/H)$. Hence this paper gives an abstract classification of embeddings of symmetric homogeneous spaces.
[Chen Zhijie (Shanghai)]

MSC 2000:: *14M17 Homogeneous spaces
14E25 Embeddings (algebraic varieties)
53C35 Symmetric spaces (differential geometry)
20G15 Linear algebraic groups over arbitrary fields

Keywords: classification of embeddings of symmetric homogeneous spaces

Cited in: Zbl 1185.14044

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]