Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [15 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02468559
Contributor : Jean-Pierre Demailly Connect in order to contact the contributor
Submitted on : Tuesday, March 17, 2020 - 7:31:15 PM
Last modification on : Tuesday, March 16, 2021 - 9:57:13 AM
Long-term archiving on: : Thursday, June 18, 2020 - 4:10:01 PM

Files

yang_mills_approach.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02468559, version 3
  • ARXIV : 2002.02677

Citation

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

Share

Metrics

Record views

63

Files downloads

68