On the Duals of Segre Varieties

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    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

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    Keywords

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

    ASJC Scopus subject areas

    • Algebra and Number Theory

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