TY - JOUR
T1 - Adjoint varieties and their secant varieties
AU - Kaji, Hajime
AU - Ohno, Masahiro
AU - Yasukura, Osami
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1999/3/29
Y1 - 1999/3/29
N2 - The purpose of this article is to show how the graded decomposition of complex simple Lie algebras g can be applied to studying adjoint varieties X and their secant varieties Sec X. Firstly quadratic equations defining adjoint varieties are explicitly given. Secondly it is shown that dim Sec X = 2 dim X for adjoint varieties X in two ways: one is based on Terracini's lemma, and the other is on some explicit description of Sec X in terms of an orbit of the adjoint action. Finally it is shown that the contact loci of the secant variety to its embedded tangent space have dimension two if X is adjoint.
AB - The purpose of this article is to show how the graded decomposition of complex simple Lie algebras g can be applied to studying adjoint varieties X and their secant varieties Sec X. Firstly quadratic equations defining adjoint varieties are explicitly given. Secondly it is shown that dim Sec X = 2 dim X for adjoint varieties X in two ways: one is based on Terracini's lemma, and the other is on some explicit description of Sec X in terms of an orbit of the adjoint action. Finally it is shown that the contact loci of the secant variety to its embedded tangent space have dimension two if X is adjoint.
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U2 - 10.1016/S0019-3577(99)80004-4
DO - 10.1016/S0019-3577(99)80004-4
M3 - Article
AN - SCOPUS:0033614166
VL - 10
SP - 45
EP - 57
JO - Indagationes Mathematicae
JF - Indagationes Mathematicae
SN - 0019-3577
IS - 1
ER -