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

Michael R. Douglas·Robert L. Karp·Sergio Lukic·Rene Reinbacher
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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.

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Michael R. Douglas, Robert L. Karp, Sergio Lukic, Rene Reinbacher. 2006-07-18. Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic. https://doi.org/10.1088/1126-6708%2F2007%2F12%2F083

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