English

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.

Keywords

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

R2 v1 2026-06-22T07:29:45.257Z