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

Michael R. Douglas et al JHEP12(2007)083   doi: 10.1088/1126-6708/2007/12/083  Help

Open Access This is an Open Access article.

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Michael R. Douglas1,2, Robert L. Karp1, Sergio Lukic1 and René Reinbacher1
1 Department of Physics, Rutgers University, Piscataway, NJ 08854-8019, U.S.A.
2 I.H.E.S., Le Bois-Marie, Bures-sur-Yvette, 91440, France
E-mail: karp@rci.rutgers.edu

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.

Key words: Statistical Methods; Differential and Algebraic Geometry

E-print number: hep-th/0606261
Cited: by
Refers: to

Received 28 November 2007, accepted for publication 14 December 2007
Published 20 December 2007

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