Spherical varieties of type A
type: Item
instance of: scholarly article
title: Spherical varieties of type A
zbMATH Open document ID: 1085.14039
author: D. Luna
published in: Publications Mathématiques
publication date: 2003-03-20T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/104178
review text: If \(G\) is a reductive group over an algebraically closed field of characteristic zero, an algebraic normal \(G\)-variety \(X\) is called spherical if it contains an open orbit of a Borel subgroup \(B\) of \(G\). In this article, the author gives a complete classification of spherical varieties for reductive groups of type A. If \(X\) is homogeneous, isomorphic to \(G/H\), then \(H\) is called a spherical subgroup of \(G\). A general spherical variety contains an open orbit isomorphic to a homogeneous spherical variety \(G/H\). Given a specific spherical homogeneous variety \(G/H\), the classification of spherical embeddings having an open orbit isomorphic to \(G/H\) is given by combinatorial data, called colored fans. This part of the classification has already been treated by the author and others. In the present article, the author classifies all homogeneous spherical varieties and their colored fans by means of combinatorial structures given on the root systems of the groups of type A. The main part of the article is devoted to the classification of wonderful varieties of type A.
reviewed by: Lucy Moser-Jauslin
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 32M12
Mathematics Subject Classification ID: 57S20
zbMATH DE Number: 1874458
zbMATH Keywords: spherical variety
zbMATH Keywords: spherical subgroup
zbMATH Keywords: reductive groups
zbMATH Keywords: wonderful variety
MaRDI profile type: Publication
OpenAlex ID: W2322154164
DOI: 10.1007/S10240-001-8194-0
description: scientific article; zbMATH DE number 1874458