Nahm transform of Higgs bundless on Riemann surface of genus at least two / Transformada de Nahm de fibrados de Higgs sobre superficies de Riemann de genero ao menos dois

AUTOR(ES)

Pedro Frejlich

DATA DE PUBLICAÇÃO

2006

RESUMO

We construct the Nahm transform of a stable, degree-zero Higgs bundle on a Riemann surface of genus at least 2. Atiyah-Singer?s index theorem is the basic tool employed, along with a vanishing theorem which is due to the stability hypothesis. Our main result is that the transformed bundle is hyperholomorphic and without flat factors. This not only recovers the algebraic results of [7] and that of [12] for the cos q = 0, but also provides a more detailed description of the geometric structure of the transformed bundle. Such results suggest that this Nahm transform can be inverted, cf. [10]. Key-words:Riemann surfaces, Stable bundles, Index Theory, Nahm Transform, Fourier-Mukai Transform, Hyperk¨ahler manifolds, Abelian varieties, Hyperholomorphic connections

ASSUNTO(S)

algebraic curves abelian varieties curvas algebricas variedades abelianas fibre spaces (mathematics) espaços fibrados (matematica)

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