On the Cartwright-Steger surface

Donald Cartwright (1) , Vincent Koziarz (2) , Sai-Kee Yeung (3)

1 University of Sydney, Sydney NSW 2006 Australia
2 IMB - Institut de Mathématiques de Bordeaux
3 Dept of Maths, Purdue University, West Lafayette, IN 47907, USA

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.

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Donald Cartwright, Vincent Koziarz, Sai-Kee Yeung. On the Cartwright-Steger surface. 2017. ⟨hal-01429836⟩