On the Picard number of rationally quartic connected manifolds

Taku Suzuki

    Research output: Contribution to journalArticle

    Abstract

    In this paper, we study structures of smooth complex projective polarized manifolds (X, H) of dimension n ≥ 2 which are rationally connected with respect to a family of H-degree four. Under the assumption (-K<inf>X</inf> · ) ≥ n + 3, we prove that, with two kinds of exceptions, the Picard number of X is at most four and X is covered by rational curves of H-degree one. In addition, we provide a classification in case n = 2.

    Original languageEnglish
    Article number1450109
    JournalInternational Journal of Mathematics
    Volume25
    Issue number12
    DOIs
    Publication statusPublished - 2014 Nov 16

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    Keywords

    • covered by lines
    • Picard number
    • rational curves
    • Rationally connected manifolds

    ASJC Scopus subject areas

    • Mathematics(all)

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