Abstract
A conjecture of Ehrenpreis states that any two compact Riemann surfaces of genus at least two have finite degree unbranched holomorphic covers that are arbitrarily close to each other in moduli space. Here we prove a weaker result where certain branched covers associated with arithmetic Riemann surfaces are allowed, and investigate the connection of our result with the original conjecture.
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The first author is supported by the Center of Excellence “Geometric Analysis and Mathematical Physics” of the Academy of Finland
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Parkkonen, J., Ruuska, V. Finite Degree Holomorphic Covers of Compact Riemann Surfaces. Acta Math Sinica 23, 89–94 (2007). https://doi.org/10.1007/s10114-005-0824-x
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DOI: https://doi.org/10.1007/s10114-005-0824-x