Preprints, Working Papers, ... Year : 2020

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

Jean-Pierre Demailly

Abstract

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.
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Dates and versions

hal-02468559 , version 1 (05-02-2020)
hal-02468559 , version 2 (24-02-2020)
hal-02468559 , version 3 (17-03-2020)
hal-02468559 , version 4 (12-02-2021)

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Jean-Pierre Demailly. Hermitian-Yang-Mills approach to the conjecture of Griffiths on the positivity of ample vector bundles. 2020. ⟨hal-02468559v3⟩
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