Closures of \(\text{SL}(2)\)-orbits in projective spaces
type: Item
instance of: scholarly article
title: Closures of \(\text{SL}(2)\)-orbits in projective spaces
zbMATH Open document ID: 0851.20041
DOI: 10.1007/BF02570476
published in: Manuscripta Mathematica
publication date: 1995-08-29T00:00:00Z
full work available at URL: https://eudml.org/doc/156089
review text: Let \(G = \text{SL} (2,\mathbb{C})\), and \(B\) a Borel subgroup. The author describes the closure of \(G\)-orbits and \(B\)-orbits in \(P(V)\), \(V\) being a regular \(G\)-module, by means of simple combinatorial data. The author also gives a criterion for determining whether the number of orbits in an orbit-closure is finite or not.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 14L35
Mathematics Subject Classification ID: 14N10
Mathematics Subject Classification ID: 20G20
zbMATH DE Number: 784076
zbMATH Keywords: closure of orbits
zbMATH Keywords: regular module
zbMATH Keywords: Borel subgroup
zbMATH Keywords: number of orbits
author: F. Pauer
reviewed by: V. Lakshmibai
MaRDI profile type: Publication
cites work: Linear orbits of d-tuples of points in P^1
cites work: Q3699843
cites work: Smooth embeddings of \(SL(2)\) and \(PGL(2)\)
cites work: Q3686804
cites work: Plongements d'espaces homogènes
cites work: Q5752670
cites work: QUASIHOMOGENEOUS AFFINE ALGEBRAIC VARIETIES OF THE GROUPSL(2)
cites work: Structure of the closure of orbits in spaces of finite-dimensional linear SL(2) representations
cites work: Conjugacy classes in algebraic groups. Notes by Vinay V. Deodhar
Recommended article: On orbital variety closures in \(\mathfrak{sl}_n\). III: Geometric properties
Recommended article: On orbital variety closures in \(\mathfrak{sl}_n\). II: Descendants of a Richardson orbital variety.
Recommended article: The combinatorics of orbital varieties closures of nilpotent order 2 in \(\text{sl}_ n\)
Recommended article: On complete orbit spaces of SL(2) actions
Recommended article: Invariant deformations of orbit closures in 𝔰𝔩(𝔫)
Recommended article: On SL(2)-orbit theorems
Recommended article: On orbital variety closures in \(\mathfrak{sl}_n\). I: Induced Duflo order.
Recommended article: Isolation, equidistribution, and orbit closures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space
Recommended article: On complete orbit spaces of SL(2) actions, II
Recommended article: Variations on the real projective orbits of \(\text{SL}(2,\mathbb Z)\) and \(\text{GL}(2,\mathbb Z)\)
description: scientific article; zbMATH DE number 784076