Arithmeticity of Some Monodromy Groups

  • T. N. VenkataramanaEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 245)


Deligne and Mostow used families of cyclic coverings of the projective line to obtain non-arithmetic monodromy and non-arithmetic lattices. In their construction, the number of ramification points is less than the degree of the cover. In contrast, we show that if the number of ramification points exceeds the degree of the cover, the monodromy group is almost always arithmetic.


Monodromy Thin groups Arithmetic groups Hermitian forms 

1991 Mathematics Subject Classification

Primary: 22E40 Secondary: 20F36 



My hearty thanks to the organisers of the conference in Bonn (in honour of Joachim Schwermer) for their kind invitation to take part in the conference, to speak there and contribute to the conference proceedings. I also thank the Max Planck Institute and the organisers for their warm hospitality. My best wishes to Joachim Schwermer.

It is a pleasure to thank the referee for a careful reading of the manuscript and for very helpful suggestions which have made a considerable improvement in the exposition of the paper.

The support of the J.C Bose fellowship for the period 2013-2018 is gratefully acknowledged.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsTata Institute of Fundamental ResearchColabaIndia

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