Deformation theory of parabolic representation pairs
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912930611593216 |
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| author | Hu, Zhi Huang, Pengfei Yan, Wanmin Zong, Runhong |
| author_facet | Hu, Zhi Huang, Pengfei Yan, Wanmin Zong, Runhong |
| contents | In this paper, we introduce the notions of parabolic representation pair variety and relative representation variety of a given parabolic type. We investigate the local behavior of these varieties. The Zariski tangent space and the tangent quadratic cones are described. By the Riemann--Hilbert--Deligne correspondence, we pro-represent the analytic germs of these varieties by functors related to certain groupoids of parabolic logarithmic flat bundles. Under suitable assumptions, we prove that the differential graded Lie algebra (DGLA) controlling the deformation of parabolic logarithmic flat bundle is mixedly formal. Finally, we construct the moduli space of weighted parabolic representation pairs, and, by means of quiver representation theory, we establish the Kobayashi--Hitchin-type theorem for polystable parabolic representation pairs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20791 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deformation theory of parabolic representation pairs Hu, Zhi Huang, Pengfei Yan, Wanmin Zong, Runhong Algebraic Geometry Representation Theory In this paper, we introduce the notions of parabolic representation pair variety and relative representation variety of a given parabolic type. We investigate the local behavior of these varieties. The Zariski tangent space and the tangent quadratic cones are described. By the Riemann--Hilbert--Deligne correspondence, we pro-represent the analytic germs of these varieties by functors related to certain groupoids of parabolic logarithmic flat bundles. Under suitable assumptions, we prove that the differential graded Lie algebra (DGLA) controlling the deformation of parabolic logarithmic flat bundle is mixedly formal. Finally, we construct the moduli space of weighted parabolic representation pairs, and, by means of quiver representation theory, we establish the Kobayashi--Hitchin-type theorem for polystable parabolic representation pairs. |
| title | Deformation theory of parabolic representation pairs |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2509.20791 |