Finiteness of hyperelliptic and superelliptic curves with CM Jacobians
Number Theory
2016-11-28 v1 Algebraic Geometry
Abstract
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 to isomorphism there are at most finitely many superelliptic curves of fixed genus with CM Jacobians. The proof relies on the geometric structures of Shimura subvarieties in Siegel modular varieties and the stability properties of Higgs bundles associated to fibred surfaces.
Keywords
Cite
@article{arxiv.1611.08477,
title = {Finiteness of hyperelliptic and superelliptic curves with CM Jacobians},
author = {Ke Chen and Xin Lu and Kang Zuo},
journal= {arXiv preprint arXiv:1611.08477},
year = {2016}
}