Hodge metrics and positivity of direct images
Hodge metrics and positivity of direct images
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DOI：
10.1515/crelle.2007.039
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发表时间：
2005-05
期刊：
影响因子：
--
通讯作者：
Christophe Mourougane;S. Takayama
中科院分区：
文献类型：
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作者：
Christophe Mourougane;S. Takayama
摘要基于Fujita-Griffiths计算Hodge丛度量的方法，我们证明了伴随半样本线丛的射影浸没直像具有Griffiths半正曲率的连续度量。这表明，对于复流形上的每个全纯半充分向量丛E，以及每个正整数k，向量丛SkE det E具有Griffiths半正曲率的连续度量。如果E在射影流形上是充分的，则度量可以是光滑的，Griffiths是正的。
Abstract Building on Fujita-Griffiths method of computing metrics on Hodge bundles, we show that the direct image of an adjoint semi-ample line bundle by a projective submersion has a continuous metric with Griffiths semi-positive curvature. This shows that for every holomorphic semi-ample vector bundle E on a complex manifold, and every positive integer k, the vector bundle SkE ⊗ det E has a continuous metric with Griffiths semi-positive curvature. If E is ample on a projective manifold, the metric can be made smooth and Griffiths positive.