The Oort conjecture for Shimura curves of small unitary rank
Algebraic Geometry
2017-12-12 v1
Abstract
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 satisfies a numerical upper bound. As an application we show that the Coleman-Oort conjecture holds for Shimura curves associated to partial corestriction upon a suitable choice of parameters, which generalizes a construction due to Mumford.
Keywords
Cite
@article{arxiv.1712.03674,
title = {The Oort conjecture for Shimura curves of small unitary rank},
author = {Ke Chen and Xin Lu and Kang Zuo},
journal= {arXiv preprint arXiv:1712.03674},
year = {2017}
}
Comments
any comment is welcome