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

Wing Keung To, Lin Weng

研究成果: ジャーナルへの寄稿 › 記事

抄録

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.

元の言語英語
ページ（範囲）2685-2707
ページ数23
ジャーナルTransactions of the American Mathematical Society
巻356
発行部数7
DOI
出版物ステータス出版済み - 7 1 2004

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Abelian Variety
Flatness
Metric
Compact Manifold
Parameter Space
Line Bundle
Vector Bundle
Curvature
Family

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

これを引用

L 2-metrics, projective flatness and families of polarized abelian varieties. / To, Wing Keung; Weng, Lin.

：: Transactions of the American Mathematical Society, 巻 356, 番号 7, 01.07.2004, p. 2685-2707.

研究成果: ジャーナルへの寄稿 › 記事

To, WK & Weng, L 2004, 'L 2-metrics, projective flatness and families of polarized abelian varieties', Transactions of the American Mathematical Society, 巻. 356, 番号 7, pp. 2685-2707. https://doi.org/10.1090/S0002-9947-03-03488-3
To WK, Weng L. L 2-metrics, projective flatness and families of polarized abelian varieties. Transactions of the American Mathematical Society. 2004 7 1;356(7):2685-2707. https://doi.org/10.1090/S0002-9947-03-03488-3
To, Wing Keung ; Weng, Lin. / L 2-metrics, projective flatness and families of polarized abelian varieties. ：: Transactions of the American Mathematical Society. 2004 ; 巻 356, 番号 7. pp. 2685-2707.
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