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 P^2. In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic.

arXiv comment25 pages, 2 figures

References in corpus (1)

• Numerical Ricci-flat metrics on K3

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