Higgs bundles twisted by a vector bundle
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916299369611264 |
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| author | Gallego, Guillermo Garcia-Prada, Oscar Narasimhan, M. S. |
| author_facet | Gallego, Guillermo Garcia-Prada, Oscar Narasimhan, M. S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_05543 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Higgs bundles twisted by a vector bundle Gallego, Guillermo Garcia-Prada, Oscar Narasimhan, M. S. Algebraic Geometry Differential Geometry Primary 14H60, Secondary 14D23, 53C07 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. |
| title | Higgs bundles twisted by a vector bundle |
| topic | Algebraic Geometry Differential Geometry Primary 14H60, Secondary 14D23, 53C07 |
| url | https://arxiv.org/abs/2105.05543 |