Hermitian-Yang-Mills approach to the conjecture of Griffiths on the positivity of ample vector bundles

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 curv...

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Bibliographic Details
Published in:Sbornik. Mathematics 2021-03, Vol.212 (3), p.305-318
Main Author: Demailly, J.-P.
Format: Article
Language:English
Subjects:
Curvature
Differential equations
Elliptic functions
Mathematical analysis
Tensors
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Summary: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.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM9387