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

Wing Keung To, Lin Weng

Research output: Contribution to journalArticlepeer-review

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 1 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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