On the Duals of Segre Varieties

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    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?

    Original languageEnglish
    Pages (from-to)221-229
    Number of pages9
    JournalGeometriae Dedicata
    Volume99
    Issue number1
    DOIs
    Publication statusPublished - 2003 Jun

    Fingerprint

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

    Keywords

    • Dual variety
    • Gauss map
    • Reflexivity
    • Segre variety
    • Symmetric matrix

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

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

    In: Geometriae Dedicata, Vol. 99, No. 1, 06.2003, p. 221-229.

    Research output: Contribution to journalArticle

    Kaji, Hajime. / On the Duals of Segre Varieties. In: Geometriae Dedicata. 2003 ; Vol. 99, No. 1. pp. 221-229.
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