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Quantitative finiteness for maximal complex totally geodesic submanifolds of non-arithmetic ball quotients
Tianzhi Hu, Runze Zhang
We prove that the number of maximal complex totally geodesic submanifolds of a smooth finite-volume non-arithmetic ball quotient is bounded linearly by its volume, with a constant…
Simpson's closedness conjecture in arbitrary rank
Tianzhi Hu
For a compact Riemann surface , Simpson associated to each stable graded Higgs bundle a locus , consisting of flat bundles th…
On the algebraicity of non-abelian Noether-Lefschetz loci of rank-two real local systems
Tianzhi Hu, Kang Zuo
As a non-abelian analogue of the Hodge locus, Simpson introduced the non-abelian Noether--Lefschetz locus and conjectured its algebraicity for PVHS. In this paper, we st…
Isomonodromic deformations of Higgs bundles and characterization of the non-abelian Noether--Lefschetz locus
Tianzhi Hu, Ruiran Sun, Jinbang Yang +1
Let be a smooth proper family of smooth projective varieties. An irreducible complex local system on a fiber admits an isomonodromic deformation, hence determines a holo…
Higher order isomonodromic deformation of Higgs bundles and a characterization of the non-abelian Noether-Lefschetz locus
Tianzhi Hu, Ruiran Sun, Jinbang Yang +1
The purpose of this paper is to establish a local theory of the non-abelian Noether--Lefschetz locus. Given a family of projective manifolds over a complex variety , the isomono…
Non-Abelian Kodaira-Spencer Map and non-existence of holomorphic isomonodromic deformation of Higgs bundles over Teichmüller spaces
Tianzhi Hu, Ruiran Sun, Kang Zuo
We define the isomonodromic deformation of a Higgs bundle on a compact Riemann surface via the Hitchin--Simpson correspondence and the isomonodromic deformation of the associated l…
Kodaira-Spencer Map on the Hitchin-Simpson Correspondence
Tianzhi Hu, Ruiran Sun, Kang Zuo
We define the isomonodromic deformation of a Higgs bundle over a compact Riemann surface via the Hitchin-Simpson correspondence and the isomonodromic deformation of a local system.…
On the distribution of non-rigid families in the moduli spaces
Ke Chen, Tianzhi Hu, Ruiran Sun +1
This paper investigates the distribution of non-rigid families in a moduli space of polarized projective manifolds for which the infinitesimal Torelli theorem holds.…