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Simpson filtrations and closure relations of Hodge moduli spaces
Zhi Hu, Pengfei Huang, Fei Yu
In this paper, we study closure relations of Simpson strata in Hodge moduli spaces over a smooth complex projective curve of genus and prove in every rank that the Heinlot…
A counterexample to the curve semistability conjecture for Higgs bundles
Pengfei Huang
In this paper, we give a counterexample to the Bruzzo--Graña Otero conjecture on the curve semistability for Higgs bundles. Let be a very general smooth plane quintic curve and…
Tangent discontinuity in the oper stratification of de Rham moduli spaces
Pengfei Huang
Let be a smooth complex projective curve of genus , and let be the moduli space of flat bundles of rank . Over the stable locus, Simpson…
Deformation theory of parabolic representation pairs
Zhi Hu, Pengfei Huang, Wanmin Yan +1
In this paper, we introduce the notions of parabolic representation pairs and the parabolic representation pair variety. We investigate the deformation theory of parabolic represen…
Rigid -connections and nilpotency of -curvatures
Pengfei Huang, Yichen Qin, Hao Sun
Motivated by Simpson's conjecture on the motivicity of rigid irreducible connections, Esnault and Groechenig demonstrated that the mod- reductions of such connections on smooth…
Parahoric reduction theory of formal connections (or Higgs fields)
Zhi Hu, Pengfei Huang, Ruiran Sun +1
In this paper, we establish the parahoric reduction theory of formal connections (or Higgs fields) on a formal principal bundle with parahoric structures, which generalizes Babbitt…
Filtered Stokes G-local Systems in Nonabelian Hodge Theory on Curves
Pengfei Huang, Hao Sun
In the wild nonabelian Hodge correspondence on curves, filtered Stokes G-local systems are regarded as the objects on the Betti side. In this paper, we demonstrate a construction o…
Moduli Spaces of Filtered G-local Systems on Curves
Pengfei Huang, Hao Sun
In this paper, we construct the moduli spaces of filtered -local systems on curves for an arbitrary reductive group over an algebraically closed field of characteristic zero…