Integral varieties of the canonical cone structure on \(G/P\)
type: Item
instance of: scholarly article
title: Integral varieties of the canonical cone structure on \(G/P\)
zbMATH Open document ID: 1072.32012
author: Insong Choe
author: Jaehyun Hong
published in: Mathematische Annalen
publication date: 2004-12-29T00:00:00Z
review text: For every point \(x\) in a compact symmetric Hermitian space \(M=G/P\), the associated cone \(K_x\) in \(T_xM\) is by definition the cone of highest weight vectors under the action of the reductive part of the parabolic subgroup \(P\). It is known that the cone \(K_x\) coincides with the cone of the vectors tangent to the lines in \(G/P\) passing through \(x\). \(K\) is the union of the \(K_x\). An integral subvariety \(X\) of \(K\) is a subvariety of \(M\) such that the tangent bundle for the smooth part is included in \(K\). \(M\) can also be imbedded equivariantly in some canonical projective space. In view of this, \(K_x\) coincides with \(M\cap T_xM\). Under this embedding, the authors give an answer to the question: When is an integral subvariety contained in a linear space on \(M\)? The authors prove that the answer is positive when \(G\) is not of type \(B_n\) or \(C_n\) and when the dimension of \(X\) is bigger than some number \(d\) depending on \(M\).
Mathematics Subject Classification ID: 32M15
Mathematics Subject Classification ID: 17B56
zbMATH DE Number: 2123986
zbMATH Keywords: compact Hermitian symmetric space
zbMATH Keywords: integral variety
reviewed by: Bang-Yen Chen
MaRDI profile type: Publication
full work available at URL: s00208-004-0530-5
OpenAlex ID: W2066733300
DOI: 10.1007/S00208-004-0530-5
description: scientific article; zbMATH DE number 2123986