Higher Gauss maps of Veronese varieties—A generalization of Boole’s formula and degree bounds for higher Gauss map images

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    Abstract

    The image of the higher Gauss map for a projective variety is discussed. The notion of higher Gauss maps here was introduced by Fyodor L. Zak as a generalization of both ordinary Gauss maps and conormal maps. The main result is a closed formula for the degree of those images of Veronese varieties. This yields a generalization of a classical formula by George Boole on the degree of the dual varieties of Veronese varieties in 1844. As an application of our formula, degree bounds for higher Gauss map images of Veronese varieties are given.

    Original languageEnglish
    Pages (from-to)1-15
    Number of pages15
    JournalCommunications in Algebra
    DOIs
    Publication statusAccepted/In press - 2018 Feb 27

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    Keywords

    • Boole’s formula
    • degree bound
    • dual variety
    • higher Gauss map
    • Veronese variety

    ASJC Scopus subject areas

    • Algebra and Number Theory

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