Email this article Hermitian-Yang-Mills approach to the conjecture of Griffiths on the positivity of ample vector bundles
- Authors: Demailly J.1
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Affiliations:
- Institut Fourier, UFR de Mathématiques
- Issue: Vol 212, No 3 (2021)
- Pages: 39-53
- Section: Articles
- URL: https://bakhtiniada.ru/0368-8666/article/view/142351
- DOI: https://doi.org/10.4213/sm9387
- ID: 142351
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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. Bibliography: 15 titles.
About the authors
Jean-Pierre Demailly
Institut Fourier, UFR de Mathématiques
Email: jean-pierre.demailly@univ-grenoble-alpes.fr
PhD
References
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