Please use this identifier to cite or link to this item: https://doi.org/10.1090/S0002-9947-03-03488-3
Title: L 2-metrics, projective flatness and families of polarized abelian varieties
Authors: To, W.-K. 
Weng, L.
Issue Date: Jul-2004
Citation: To, W.-K., Weng, L. (2004-07). L 2-metrics, projective flatness and families of polarized abelian varieties. Transactions of the American Mathematical Society 356 (7) : 2685-2707. ScholarBank@NUS Repository. https://doi.org/10.1090/S0002-9947-03-03488-3
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.
Source Title: Transactions of the American Mathematical Society
URI: http://scholarbank.nus.edu.sg/handle/10635/103468
ISSN: 00029947
DOI: 10.1090/S0002-9947-03-03488-3
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