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A note on Demailly’s approach towards a conjecture of Griffiths. (English) Zbl 1470.32050

Summary: We prove that a “cushioned” Hermitian-Einstein-type equation proposed by Demailly in an approach towards a conjecture of Griffiths on the existence of a Griffiths positively curved metric on a Hartshorne ample vector bundle, has an essentially unique solution when the bundle is stable. This result indicates that the proposed approach must be modified in order to attack the aforementioned conjecture of Griffiths.

MSC:

32L05 Holomorphic bundles and generalizations
32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
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References:

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