Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

On the Cartwright-Steger surface


Authors: Donald I. Cartwright, Vincent Koziarz and Sai-Kee Yeung
Journal: J. Algebraic Geom. 26 (2017), 655-689
DOI: https://doi.org/10.1090/jag/696
Published electronically: April 21, 2017
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Abstract | References | Additional Information

Abstract: In this article, we study various concrete algebraic and differential geometric properties of the Cartwright-Steger surface, the unique smooth surface of Euler number 3 which is neither a projective plane nor a fake projective plane. 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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Additional Information

Donald I. Cartwright
Affiliation: School of Mathematics & Statistics, University of Sydney, Sydney, NSW 2006, Australia
Email: donald.cartwright@sydney.edu.au

Vincent Koziarz
Affiliation: Institut de Mathématiques, Université de Bordeaux, IMB, UMR 5251, F-33400 Talence, France
Email: vincent.koziarz@math.u-bordeaux.fr

Sai-Kee Yeung
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: yeung@math.purdue.edu

DOI: https://doi.org/10.1090/jag/696
Received by editor(s): June 4, 2015
Received by editor(s) in revised form: December 29, 2015, and October 13, 2016
Published electronically: April 21, 2017
Additional Notes: The third author was partially supported by a grant from the National Science Foundation
Article copyright: © Copyright 2017 University Press, Inc.

American Mathematical Society