Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic

Abstract

We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on 2. In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic. © SISSA 2007.