Deformation theory of parabolic representation pairs
Abstrak
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.
Penulis (4)
Zhi Hu
Pengfei Huang
Wanmin Yan
Runhong Zong
Akses Cepat
- Tahun Terbit
- 2025
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓