L 2-metrics, projective flatness and families of polarized abelian varieties

Wing Keung To, Lin Weng

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)

    Abstract

    We compute the curvature of the L 2-metric on the direct image of a family of Hermitian holomorphic vector bundles over a family of compact Kähler manifolds. As an application, we show that the L 2-metric on the direct image of a family of ample line bundles over a family of abelian varieties and equipped with a family of canonical Hermitian metrics is always projectively flat. When the parameter space is a compact Kähler manifold, this leads to the poly-stability of the direct image with respect to any Kähler form on the parameter space.

    Original languageEnglish
    Pages (from-to)2685-2707
    Number of pages23
    JournalTransactions of the American Mathematical Society
    Volume356
    Issue number7
    DOIs
    Publication statusPublished - Jul 2004

    All Science Journal Classification (ASJC) codes

    • General Mathematics
    • Applied Mathematics

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