11 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. Motivated by known non-rigid examples, we conjecture that a family over a quasi-projective curve…
Non-existence of Shimura curves of Mumford type generically in the non-hyperelliptic locus
Xin Lu, Shengli Tan, Kang Zuo
We show that there does not exist any Shimura curve with strictly maximal Higgs field generically in the Torelli locus of non-hyperelliptic curves of genus . In particular…
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.…
Logarithmic Crystalline Representations
Zhenmou Liu, Jinbang Yang, Kang Zuo
In 1989, Faltings proved the comparison theorem between étale cohomology and crystalline cohomology by studying Fontaine-Faltings modules and crystalline representations. In his p…