Adjoint varieties and their secant varieties

Hajime Kaji, Masahiro Ohno, Osami Yasukura

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)45-57
Number of pages13
JournalIndagationes Mathematicae
Volume10
Issue number1
DOIs
Publication statusPublished - 1999 Mar 29

ASJC Scopus subject areas

  • Mathematics(all)

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