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
    Publication statusPublished - 1999 Mar 29

    Fingerprint

    Secant Varieties
    Quadratic equation
    Tangent Space
    Simple Lie Algebra
    Locus
    Lemma
    Two Dimensions
    Orbit
    Contact
    Decompose

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Kaji, H., Ohno, M., & Yasukura, O. (1999). Adjoint varieties and their secant varieties. Indagationes Mathematicae, 10(1), 45-57.

    Adjoint varieties and their secant varieties. / Kaji, Hajime; Ohno, Masahiro; Yasukura, Osami.

    In: Indagationes Mathematicae, Vol. 10, No. 1, 29.03.1999, p. 45-57.

    Research output: Contribution to journalArticle

    Kaji, H, Ohno, M & Yasukura, O 1999, 'Adjoint varieties and their secant varieties', Indagationes Mathematicae, vol. 10, no. 1, pp. 45-57.
    Kaji H, Ohno M, Yasukura O. Adjoint varieties and their secant varieties. Indagationes Mathematicae. 1999 Mar 29;10(1):45-57.
    Kaji, Hajime ; Ohno, Masahiro ; Yasukura, Osami. / Adjoint varieties and their secant varieties. In: Indagationes Mathematicae. 1999 ; Vol. 10, No. 1. pp. 45-57.
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