15 citations · 19 across the 10 of their papers we have counts for
10 papers
The Oort conjecture for Shimura curves of small unitary rank
Ke Chen, Xin Lu, Kang Zuo
We prove that a Shimura curve in the Siegel modular variety is not generically contained in the open Torelli locus as long as the rank of unitary part in its canonical Higgs bundle…
On a question of Ekedahl and Serre
Ke Chen, Xin Lu, Kang Zuo
In this paper we study various aspects of the Ekedahl-Serre problem. We formulate questions of Ekedahl-Serre type and Coleman-Oort type for general weakly special subvarieties in t…
Finiteness of hyperelliptic and superelliptic curves with CM Jacobians
Ke Chen, Xin Lu, Kang Zuo
In this paper we study the Coleman-Oort conjecture for superelliptic curves, i.e., curves defined by affine equations with a separable polynomial. We prove that up t…
On Higgs bundles over Shimura varieties of ball quotient type
Ke Chen, Xin Lu, Sheng-Li Tan +1
We prove the generic exclusion of certain Shimura varieties of unitary and orthogonal types from the Torelli locus. The proof relies on a slope inequality on surface fibration due…
A note on Shimura subvarieties in the hyperelliptic Torelli locus
Ke Chen, Xin Lu, Kang Zuo
We prove the non-existence of Shimura subvarieties of positive dimension contained generically in the hyperelliptic Torelli locus for curves of genus at least 8, which is an analog…
Bounded eqidistribution of special subvarieties in mixed Shimura varieties
Ke Chen
In this paper we prove the equidistribution of bounded sequences of special subvarieties in a general mixed Shimura varieties, a notion adapted from the pure case treated by Clozel…
On the Oort conjecture for Shimura varieties of unitary and orthogonal types
Ke Chen, Xin Lu, Kang Zuo
In this paper we study the Oort conjecture on Shimura subvarieties contained generically in the Torelli locus in the Siegel modular variety . Using the poly-stabilit…
A note on the Manin-Mumford conjecture
K. Chen
In this paper we prove a special case of the André-Oort conjecture for Kuga varieties. If is a Kuga variety fibred over a pure Shimura variety as an abelian scheme, and $(M…
On special subvarieties of Kuga varieties II
K. Chen
In this paper we prove the equidistribution of $\Cbf$-special subvarieties in certain Kuga varieties, which implies a special case of the general André-Oort conjecture formulated f…
On Special Subvarieties of Kuga Varieties
K. Chen
In this paper we prove the equidistribution of certain families of special subvarieties in Kuga varieties, which is a special case of the general Andre-Oort conjecture formulated f…