TY - JOUR
T1 - L 2-metrics, projective flatness and families of polarized abelian varieties
AU - To, Wing Keung
AU - Weng, Lin
N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2004/7
Y1 - 2004/7
N2 - 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.
AB - 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.
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U2 - 10.1090/S0002-9947-03-03488-3
DO - 10.1090/S0002-9947-03-03488-3
M3 - Article
AN - SCOPUS:2942638029
VL - 356
SP - 2685
EP - 2707
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 7
ER -