On the Cartwright-Steger surface
Algebraic Geometry
2015-03-12 v2 Complex Variables
Abstract
In this article, we study various concrete algebraic and differential geometric properties of the Cartwright-Steger surface. In particular, we determine the genus of a generic fiber of the Albanese fibration, and deduce that the singular fibers are not totally geodesic, answering an open problem about fibrations of a complex ball quotient over a Riemann surface.
Cite
@article{arxiv.1412.4137,
title = {On the Cartwright-Steger surface},
author = {Donald I. Cartwright and Vincent Koziarz and Sai-Kee Yeung},
journal= {arXiv preprint arXiv:1412.4137},
year = {2015}
}
Comments
A longer version of this paper, which contains some geometric results we have omitted here, provides more details of some calculations, and adopts a different approach to proving some results, can be found on the webpage of the first named author (see reference [CKY]). It is an update of version 1 of this paper