Multiplicative Higgs bundles and involutions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866914848366919680 |
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| author | Gallego, Guillermo Garcia-Prada, Oscar |
| author_facet | Gallego, Guillermo Garcia-Prada, Oscar |
| contents | In this paper we generalize the theory of multiplicative $G$-Higgs bundles over a curve to pairs $(G,θ)$, where $G$ is a reductive algebraic group and $θ$ is an involution of $G$. This generalization involves the notion of a multiplicative Higgs bundle taking values in a symmetric variety associated to $θ$, or in an equivariant embedding of it. We also study how these objects appear as fixed points of involutions of the moduli space of multiplicative $G$-Higgs bundles, induced by the involution $θ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02553 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multiplicative Higgs bundles and involutions Gallego, Guillermo Garcia-Prada, Oscar Algebraic Geometry 14D23 (Primary) 14H60, 14M17 (Secondary) In this paper we generalize the theory of multiplicative $G$-Higgs bundles over a curve to pairs $(G,θ)$, where $G$ is a reductive algebraic group and $θ$ is an involution of $G$. This generalization involves the notion of a multiplicative Higgs bundle taking values in a symmetric variety associated to $θ$, or in an equivariant embedding of it. We also study how these objects appear as fixed points of involutions of the moduli space of multiplicative $G$-Higgs bundles, induced by the involution $θ$. |
| title | Multiplicative Higgs bundles and involutions |
| topic | Algebraic Geometry 14D23 (Primary) 14H60, 14M17 (Secondary) |
| url | https://arxiv.org/abs/2304.02553 |