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Hodge metrics and positivity of direct images
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August 7, 2007
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.
Received: 2005-12-01
Revised: 2006-03-21
Published Online: 2007-08-07
Published in Print: 2007-06-27
© Walter de Gruyter
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Articles in the same Issue
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- Anticyclotomic main conjectures for CM modular forms
- On the faithfulness of parabolic cohomology as a Hecke module over a finite field
- On the Maillet-Baker continued fractions
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- A cohomological stability result for projective schemes over surfaces
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Extension operators for real analytic functions on compact subvarieties of
- Correction to the paper: Convergence properties of the Yang-Mills flow on Kähler surfaces
