Tangent loci and certain linear sections of adjoint varieties

Hajime Kaji, Osami Yasukura

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    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

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    ASJC Scopus subject areas

    • Mathematics(all)

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