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

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Published 20 December 2007 Published under licence by IOP Publishing Ltd
, , Citation Michael R. Douglas et al JHEP12(2007)083 DOI 10.1088/1126-6708/2007/12/083

1126-6708/2007/12/083

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 Bbb P2. In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic.

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10.1088/1126-6708/2007/12/083