On the Cartwright-Steger surface

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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.

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Publication date Created: 12 December 2014

Publication date Updated: 2015-03-10

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ArXiV ID: 1412.4137

SO-VID: 6abc7129-4171-4d22-90e0-08ef30575f2c

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http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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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

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On the Cartwright-Steger surface

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Numerical Algebra, Matrix Theory, Differential-Algebraic Equations, and Control Theory

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