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

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

2006-06-27

arxiv.org/abs/hep-th/0606261v2

JHEP0712:083,2007

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 2 figures

Scientific paper

10.1088/1126-6708/2007/12/083

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.

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