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Prym covers, theta functions and Kobayashi curves in Hilbert modular surfaces
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 136, Number 4, August 2014
- pp. 995-1021
- 10.1353/ajm.2014.0026
- Article
- Additional Information
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Algebraic curves in Hilbert modular surfaces that are totally geodesic for the Kobayashi metric have
very interesting geometric and arithmetic properties, e.g., they are rigid. There are very few methods
known to construct such algebraic geodesics that we call Kobayashi curves. We give an explicit way of
constructing Kobayashi curves using determinants of derivatives of theta functions. This construction
also allows to calculate the Euler characteristics of the Teich\-m\"uller curves constructed by McMullen
using Prym covers.