Geodesic
Hermitian-Yang-Mills approach to the conjecture of Griffiths on the positivity of ample vector bundles
Sbornik. Mathematics, Tome 212 (2021) no. 3, pp. 305-318

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Given a vector bundle of arbitrary rank with ample determinant line bundle on a projective manifold, we propose a new elliptic system of differential equations of Hermitian-Yang-Mills type for the curvature tensor. The system is designed so that solutions provide Hermitian metrics with positive curvature in the sense of Griffiths — and even in the dual Nakano sense. As a consequence, if an existence result could be obtained for every ample vector bundle, the Griffiths conjecture on the equivalence between ampleness and positivity of vector bundles would be settled. Bibliography: 15 titles.
Keywords: ample vector bundle, Griffiths positivity, Hermitian-Yang-Mills equation. 
@article{SM_2021_212_3_a3,
     author = {J.-P. Demailly},
     title = {Hermitian-Yang-Mills approach to the conjecture of {Griffiths} on the positivity of ample vector bundles},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {212},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2021_212_3_a3/}
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J.-P. Demailly. Hermitian-Yang-Mills approach to the conjecture of Griffiths on the positivity of ample vector bundles. Sbornik. Mathematics, Tome 212 (2021) no. 3, pp. 305-318. http://geodesic.mathdoc.fr/item/SM_2021_212_3_a3/