Tangent loci and certain linear sections of adjoint varieties

Hajime Kaji, Osami Yasukura

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    An adjoint variety X (g) associated to a complex simple Lie algebra g is by definition a projective variety in ℙ*(g) obtained as the projectivization of the (unique) non-zero, minimal nilpotent orbit in g. We first describe the tangent loci of X (g) in terms of s-fraktur sign and l-fraktur sign2-triples. Secondly for a graded decomposition of contact type g = ⊕-2≤i≤2gi, we show that the intersection of X (g) and the linear subspace ℙ*(g1) in ℙ*(g) coincides with the cubic Veronese variety associated to g.

    Original languageEnglish
    Pages (from-to)63-72
    Number of pages10
    JournalNagoya Mathematical Journal
    Volume158
    Publication statusPublished - 2000 Jun

    Fingerprint

    Nilpotent Orbits
    Simple Lie Algebra
    Projective Variety
    Tangent line
    Locus
    Intersection
    Subspace
    Contact
    Decompose

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Tangent loci and certain linear sections of adjoint varieties. / Kaji, Hajime; Yasukura, Osami.

    In: Nagoya Mathematical Journal, Vol. 158, 06.2000, p. 63-72.

    Research output: Contribution to journalArticle

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