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|Title:||L 2-metrics, projective flatness and families of polarized abelian varieties|
|Authors:||To, W.-K. |
|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|
|Appears in Collections:||Staff Publications|
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