Homogeneous projective varieties with degenerate secants

    Research output: Contribution to journalArticle

    10 Citations (Scopus)

    Abstract

    The secant variety of a projective variety X in ℙ, denoted by SecX, is denned to be the closure of the union of lines in ℙ passing through at least two points of X, and the secant deficiency of X is defined by δ := 2 dim X + 1 -dim Sec X. We list the homogeneous projective varieties X with δ > 0 under the assumption that X arise from irreducible representations of complex simple algebraic groups. It turns out that there is no homogeneous, non-degenerate, projective variety X with SecX 5 P and δ > 8, and the E6-variety is the only homogeneous projective variety with largest secant deficiency δ = 8. This gives a negative answer to a problem posed by R. Lazarsfeld and A. Van de Ven if we restrict ourselves to homogeneous projective varieties.

    Original languageEnglish
    Pages (from-to)533-545
    Number of pages13
    JournalTransactions of the American Mathematical Society
    Volume351
    Issue number2
    Publication statusPublished - 1999

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    Projective Variety
    Chord or secant line
    Secant Varieties
    Algebraic Groups
    Simple group
    Irreducible Representation
    Closure
    Union
    Line

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Homogeneous projective varieties with degenerate secants. / Kaji, Hajime.

    In: Transactions of the American Mathematical Society, Vol. 351, No. 2, 1999, p. 533-545.

    Research output: Contribution to journalArticle

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