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

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    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

    Fingerprint

    Gauss Map
    Projective Variety
    Closed
    Generalization

    Keywords

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

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    @article{170ee30ef849473ba0c2a5d9dd533452,
    title = "Higher Gauss maps of Veronese varieties—A generalization of Boole’s formula and degree bounds for higher Gauss map images",
    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.",
    keywords = "Boole’s formula, degree bound, dual variety, higher Gauss map, Veronese variety",
    author = "Hajime Kaji",
    year = "2018",
    month = "2",
    day = "27",
    doi = "10.1080/00927872.2018.1435790",
    language = "English",
    pages = "1--15",
    journal = "Communications in Algebra",
    issn = "0092-7872",
    publisher = "Taylor and Francis Ltd.",

    }

    TY - JOUR

    T1 - Higher Gauss maps of Veronese varieties—A generalization of Boole’s formula and degree bounds for higher Gauss map images

    AU - Kaji, Hajime

    PY - 2018/2/27

    Y1 - 2018/2/27

    N2 - 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.

    AB - 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.

    KW - Boole’s formula

    KW - degree bound

    KW - dual variety

    KW - higher Gauss map

    KW - Veronese variety

    UR - http://www.scopus.com/inward/record.url?scp=85042940550&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85042940550&partnerID=8YFLogxK

    U2 - 10.1080/00927872.2018.1435790

    DO - 10.1080/00927872.2018.1435790

    M3 - Article

    AN - SCOPUS:85042940550

    SP - 1

    EP - 15

    JO - Communications in Algebra

    JF - Communications in Algebra

    SN - 0092-7872

    ER -