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arXiv · 2105.05543

Higgs bundles twisted by a vector bundle

Guillermo Gallego·Oscar Garcia-Prada·M. S. Narasimhan
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Abstract

In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank 2 vector bundle. We define a Hitchin map and give a spectral correspondence. We also state a Hitchin-Kobayashi correspondence for a generalization of the Hitchin equations to this situation. In a certain sense, this theory lies halfway between the theories of Higgs bundles on a curve and on a higher dimensional variety.

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Guillermo Gallego, Oscar Garcia-Prada, M. S. Narasimhan. 2021-05-12. Higgs bundles twisted by a vector bundle. https://doi.org/10.1142/s0129167x24410076

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