12 citations · 22 across the 18 of their papers we have counts for
19 papers
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…
Rigidity Criterion for Certain Calabi-Yau Families
Ruiran Sun, Chenglong Yu, Kang Zuo
We prove a new rigidity criterion for families of polarized Calabi--Yau manifolds. If, near a boundary point, the total space is smooth, the relative canonical bundle is trivial, a…
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.…
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…
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.…
Entire holomorphic curves into intersecting general hypersurfaces
Zhangchi Chen, Dinh Tuan Huynh, Ruiran Sun +1
Let be hypersurfaces in with total degrees , in general position and satisfying a generic…
Finiteness of pointed maps to moduli spaces of polarized varieties
Ariyan Javanpeykar, Steven Lu, Ruiran Sun +1
We establish a finiteness result for pointed maps to the base space of a smooth projective family of varieties with maximal variation in moduli. For its proof, we establish the…
Hyperbolicity of varieties with big linear representation of
Ruiran Sun
We show the following algebraicity result for a complex projective variety with big representation of into a semi-simple algebraic group: There exists a proper subvariety…
Topological Hyperbolicity of Moduli spaces of Elliptic Surfaces
Xin Lü, Ruiran Sun, Kang Zuo
We introduce the notion of topological hyperbolicity to characterize the largeness of the topological fundamental group of a complex variety. Inspired by the Shafarevich conjecture…
Big Picard Theorem for jet differentials and Non-archimedean Ax-Lindemann Theorem
Dinh Tuan Huynh, Ruiran Sun, Song-Yan Xie
By implementing jet differential techniques in non-archimedean geometry, we obtain a big Picard type extension theorem, which generalizes a previous result of Cherry and Ru. As app…
Holomorphic curves in Base Spaces of Families of Polarized Manifolds
Steven Lu, Ruiran Sun, Kang Zuo
For a smooth family of polarized manifolds with semi-ample canonical sheaves, we show the following result: any entire curve must be contained in the fibers of the classi…
Non-archimedean hyperbolicity of the moduli space of curves
Ruiran Sun
Let be a complete algebraically closed non-archimedean valued field of characteristic zero, and let be a finite type scheme over . We say is -analytically Borel h…
Second Main Theorem on the Moduli Spaces of Polarized Varieties
Ruiran Sun
Let be a smooth log pair over such that the complement carries a maximally varied family of polarized manifolds. We prove a version of sec…
The Shafarevich conjecture revisited: Finiteness of pointed families of polarized varieties
Ariyan Javanpeykar, Ruiran Sun, Kang Zuo
Motivated by Lang-Vojta's conjectures on hyperbolic varieties, we prove a new version of the Shafarevich conjecture in which we establish the finiteness of pointed families of pola…
Picard theorems for moduli spaces of polarized varieties
Ya Deng, Steven Lu, Ruiran Sun +1
As a result of our study of the hyperbolicity of the moduli space of polarized manifold, we give a general big Picard theorem for a holomorphic curve on a log-smooth pair s…
Base change of twisted Fontaine-Faltings modules and Twisted Higgs-de Rham flows over very ramified valuation rings
Ruiran Sun, Jinbang Yang, Kang Zuo
In this short notes, we prove a stronger version of Theorem 0.6 in our previous paper arXiv:1709.01485: Given a smooth log scheme $(\mathcal{X} \supset \mathcal{D})_{W(\mathbb{F}_q…
Projective Crystalline Representations of Étale Fundamental Groups and Twisted Periodic Higgs-de Rham Flow
Ruiran Sun, Jinbang Yang, Kang Zuo
This paper contains three new results. {\bf 1}.We introduce new notions of projective crystalline representations and twisted periodic Higgs-de Rham flows. These new notions genera…