The Automorphism Equivariant Hitchin Index
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917081763545088 |
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| author | Andersen, Jørgen Ellegaard Mistegård, William Elbæk |
| author_facet | Andersen, Jørgen Ellegaard Mistegård, William Elbæk |
| contents | Let T be the one-dimensional complex torus. We consider the action of an automorphism of a Riemann surface X on the cohomology of the T-equivariant determinant line bundle over the moduli space of rank two Higgs bundles on X with fixed determinant of odd degree. We define and study the automorphism equivariant Hitchin index. We prove a formula for it in terms of cohomological pairings of canonical T-equivariant classes of certain moduli spaces of parabolic Higgs bundles over the quotient Riemann surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13289 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Automorphism Equivariant Hitchin Index Andersen, Jørgen Ellegaard Mistegård, William Elbæk Differential Geometry Algebraic Geometry Let T be the one-dimensional complex torus. We consider the action of an automorphism of a Riemann surface X on the cohomology of the T-equivariant determinant line bundle over the moduli space of rank two Higgs bundles on X with fixed determinant of odd degree. We define and study the automorphism equivariant Hitchin index. We prove a formula for it in terms of cohomological pairings of canonical T-equivariant classes of certain moduli spaces of parabolic Higgs bundles over the quotient Riemann surface. |
| title | The Automorphism Equivariant Hitchin Index |
| topic | Differential Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2401.13289 |