On the Cartwright-Steger surface
Donald I. Cartwright, Vincent Koziarz, Sai-Kee Yeung
TL;DR
This paper investigates the algebraic and differential geometric properties of the Cartwright-Steger surface, including the genus of fibers and the nature of singular fibers, providing new insights into its geometric structure.
Contribution
It determines the genus of a generic fiber of the Albanese fibration and shows that singular fibers are not totally geodesic, resolving an open problem.
Findings
Genus of a generic fiber of the Albanese fibration is identified.
Singular fibers are proven not to be totally geodesic.
Provides new geometric insights into the Cartwright-Steger surface.
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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