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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…
Rigidity for proper holomorphic ball maps with degenerate CR Gauss map
Tianzhi Hu, Wanke Yin, Pingsan Yuan
Let and be integers with , and let be a proper holomorphic map that admits a -smooth extension to the boundary. We pro…
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…
Pointwise energy monotonicity for stable Higgs bundles
Tianzhi Hu
We study the Dai--Li conjecture concerning the pointwise monotonicity of the energy density along the -flow of stable Higgs bundles. We prov…
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…
Sharp degree bound for rational proper maps from to
Tianzhi Hu, Mai Shi, Pingsan Yuan
We prove that every rational proper holomorphic map from to has degree at most , confirming D'Angelo's conjecture in this case. This sharp bound fo…
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…