On the Duals of Segre Varieties

    研究成果: Article

    9 引用 (Scopus)

    抄録

    The reflexivity, the (semi-)ordinariness, the dimension of dual varieties and the structure of Gauss maps are discussed for Segre varieties, where a Segre variety is the image of the product of two or more projective spaces under Segre embedding. A generalization is given to a theorem of A. Hefez and A. Thorup on Segre varieties of two projective spaces. In particular, a new proof is given to a theorem of F. Knop, G. Menzel, I. M. Gelfand, M. M. Kapranov and A. V. Zelevinsky that states a necessary and sufficient condition for Segre varieties to have codimension one duals. On the other hand, a negative answer is given to a problem raised by S. Kleiman and R. Piene as follows: For a projective variety of dimension at least two, do the Gauss map and the natural projection from the conormal variety to the dual variety have the same inseparable degree?

    元の言語English
    ページ(範囲)221-229
    ページ数9
    ジャーナルGeometriae Dedicata
    99
    発行部数1
    DOI
    出版物ステータスPublished - 2003 6

    Fingerprint

    Segre Variety
    Gauss Map
    Projective Space
    Reflexivity
    Projective Variety
    Theorem
    Codimension
    Projection
    Necessary Conditions
    Sufficient Conditions

    ASJC Scopus subject areas

    • Algebra and Number Theory

    これを引用

    On the Duals of Segre Varieties. / Kaji, Hajime.

    :: Geometriae Dedicata, 巻 99, 番号 1, 06.2003, p. 221-229.

    研究成果: Article

    Kaji, Hajime. / On the Duals of Segre Varieties. :: Geometriae Dedicata. 2003 ; 巻 99, 番号 1. pp. 221-229.
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